FACTDOUBLE in Zoho Sheet: Even and Odd Double Factorials

=FACTDOUBLE(number)

The official Zoho FACTDOUBLE help page explicitly defines the even and odd products and states that 0!!=1. It documents =FACTDOUBLE(4.6) → 8, =FACTDOUBLE(10) → 3,840 and =FACTDOUBLE(0) → 1. This differs from a common but incorrect approach that squares a factorial or applies FACT twice. The vendor does not provide an upper finite input bound, an original-support version, or a complete platform equivalence matrix.

For a positive even integer n, multiply n, n-2, n-4 and so on down to 2. For a positive odd integer n, multiply n, n-2, n-4 and so on down to 1. The zero case is defined to equal 1, giving a useful base case for the recurrence n!! = n*(n-2)!! for integer n≥2, using 0!!=1 and 1!!=1 as base cases. This recurrence is a mathematical identity, not evidence of how Zoho internally calculates the result.

Enter the double-factorial inputs below in F2:F9, with a header in F1. Type =FACTDOUBLE(F2) in H2 and fill down to H9. Check column F contains actual numeric values. The table records independently computed mathematical expectations—not native Zoho formula executions.

Start with the even case in row 4 and verify the product by hand. Then inspect the odd case in row 8 and notice that the terms decrease by two, not one. Row 6 is an important input-quality demonstration: 4.6 is truncated, not rounded to 5, so the expected output is 8 rather than 15. Fill down only after your first result is sensible and the cell format is numeric. The checked Zoho reference uses only one required function argument and therefore does not introduce a separator ambiguity inside FACTDOUBLE itself.

For a nonnegative even integer n = 2k, a mathematical identity is:

(2k)!! = 2^k × k!.

For n=10, k=5: 2^5 × 5! = 32×120 = 3,840. In spreadsheet-style notation this cross-check can be written:

=POWER(2;10/2)*FACT(10/2)

Compare the independent result with =FACTDOUBLE(10), also expected to be 3,840. With n stored in F9, the generalized expression is =POWER(2;F9/2)*FACT(F9/2). Only use that identity with even nonnegative whole-number n. For odd n, F9/2 would be fractional and the documented FACT truncation would lead to the wrong relationship. This is an educational audit formula; no combined expression was run in Zoho during this research pass.

For a positive odd integer n=2k-1, another identity is (2k-1)!! = (2k)!/(2^k × k!). Take n=9, so k=5. Compute:

=FACT(10)/(POWER(2;5)*FACT(5))

The independently expected result is 945: 9×7×5×3×1 = 945 and 10!/(32×120)=945. The corresponding direct function formula is =FACTDOUBLE(9). The identity helps catch mistakes when moving between recurrence formulas and ordinary factorial expressions. It is not a statement about Zoho’s undocumented internal calculation method, nor is it advisable for huge arguments where intermediate factorials may exceed floating-point precision even if a final ratio is modest.

Double factorials arise in mathematical counting problems, recurrence relations, selected probability formulas and expressions containing products of consecutive odd or consecutive even positive integers. For everyday inventory or billing totals, ordinary multiplication, SUM or FACT is more commonly the intended calculation. If a question says “arrange six distinct objects in order,” FACT(6) is the correct conceptual starting point; use FACTDOUBLE only when the underlying formula explicitly requires every other integer. An odd product such as 1×3×5×7×9 corresponds to FACTDOUBLE(9), not FACT(9).

Microsoft Excel’s FACTDOUBLE documentation separately documents fractional truncation and #NUM! for negative arguments. Although the mathematical even/odd products align with Zoho’s description, Excel’s native negative-number error display and potential argument limits have not been tested on Zoho. Different locale punctuation, number coercion, floating-point precision and client availability remain genuine migration checks. Do not infer Google Sheets or another spreadsheet’s behavior from the common function name alone.

Zoho’s Windows/macOS desktop beta announcement describes more than 400 built-in functions but also says some web functionality is still being added. No release-number or across-device parity claim is made for this function, and this guide does not assume that past versions supported the same boundary cases.

Official Zoho function article directly checked: October 11, 2026. Mathematical outputs: evaluated independently using Python integer products, including the even and odd identities. Native Zoho Sheet executions: 0. Screenshots: none. For the precise vendor specification see the Zoho FACTDOUBLE article and for consecutive-integer products consult the separate FACT guide.