FACTDOUBLE in Google Sheets: Alternating Products and Unordered Pairings

• Introduced: first service launch date is not established by the official history reviewed; no numbered desktop introduction is assigned.
• Availability: documented in the rolling Google Sheets service. Examples use ordinary web-spreadsheet numeric cells; other clients and imported files are not separately certified.
• Checked: October 14, 2026; official FACTDOUBLE reference. Documentation and independent calculations, without native Sheets execution.

=FACTDOUBLE(value)

The argument is a number or numeric-cell reference. Google’s dedicated help defines the step of two and explicitly says that fractional parts are truncated. A positive control of FACTDOUBLE(9.8) therefore has expected result 945.

The short reference does not establish a complete negative-input, nonnumeric or native overflow policy. This guide does not substitute Microsoft’s error table or a generalized analytic double-factorial convention for missing Sheets evidence. The successful examples use positive integer counts.

Enter 1, 2, 3, 4, 5, 6, 7, 8, 9 in A2:A10 and fill =FACTDOUBLE(A2) down.

Expected outputs are 1, 2, 3, 8, 15, 48, 105, 384, 945. An even starting value ends with a factor of two; an odd starting value ends with one. The function does not turn an odd argument into an even one before multiplying.

For example, 6!!=6×4×2=48 and 9!!=9×7×5×3×1=945. These small explicit products let you verify the operation without relying on a formula engine.

=FACTDOUBLE(6)
=2*FACT(6)
=FACT(FACT(3))

Expected results are 48, 1440 and 720. The second formula doubles 720, while the third computes the factorial of six after the inner call returns six. Neither is the alternating product of FACTDOUBLE.

The exclamation-mark notation n!! means the same alternating product in this guide. It should not be interpreted as an instruction to enter punctuation after a cell value instead of the worksheet function.

Ten labeled objects must form five unordered pairs. Choose a partner for the first label in nine ways. Eight objects remain, giving seven choices for the next smallest unpaired label, then five, three and one.

=FACTDOUBLE(10-1)

Expected number of complete pairings: 945. Pair order does not matter, and swapping the two members within one pair does not create a new pairing.

For four objects A, B, C and D, the same construction gives FACTDOUBLE(3)=3: AB/CD, AC/BD and AD/BC. This explicit small enumeration checks that the mathematical model is counting pairings rather than ordered sequences.

For five positive even factors:

=FACTDOUBLE(10)
=2^5*FACT(5)

Both expected results are 3840. Factoring two out of each term in 10×8×6×4×2 leaves 5×4×3×2×1.

The complementary odd-product check =FACT(10)/(2^5*FACT(5)) gives 945, agreeing with FACTDOUBLE(9). These identities independently verify the small examples; they do not promise equal native precision for every large factorial intermediate.

The mathematical empty-product convention assigns 0!!=1, but the zero-input native result is not separately pinned by this short reference. Negative or fractional-negative extensions should remain explicit test cases rather than assumed valid counting inputs.

Before adapting the pairing example, decide whether objects, pair members or pair order are distinguishable. Changing any of those assumptions changes the number being counted. Keep original quantities visible so silent truncation cannot conceal an invalid fractional item count.

• Google FACTDOUBLE help.
• Editorial testing standards.

Inputs are fictional. Approximate numerical answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Complete coercion, extreme-magnitude and cross-client behavior remain untested.