FACTDOUBLE in Excel: Alternating Products and Pairing Counts

• Introduced: First introduction version is not established by the official history reviewed.
• Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026; official FACTDOUBLE reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=FACTDOUBLE(number)

The required numeric input is truncated when it is not an integer. Microsoft documents #VALUE! for a nonnumeric argument and #NUM! for a negative number. The even and odd cases use different terminating products.

These formulas use English names and ordinary numeric arguments. The examples deliberately stay with positive integer counts and one positive truncation control; they do not infer an analytic extension to negative arguments from mathematical notation used elsewhere.

Enter 1, 2, 3, 4, 5, 6, 7, 8 in A2:A9. Fill =FACTDOUBLE(A2) down.

Expected outputs are 1, 2, 3, 8, 15, 48, 105, 384. The step is two, so 7 produces 7×5×3×1=105, while 8 produces 8×6×4×2=384. The odd case does not first round upward to an even input.

For the documented truncation rule, =FACTDOUBLE(8.7) has expected result 384. Treat a fractional item count as a validation issue in a counting model rather than relying on truncation to repair it silently.

=FACTDOUBLE(4)
=2*FACT(4)
=FACT(FACT(3))

Expected results are 8, 48 and 720. The first is 4×2. The second doubles 24. The third computes FACT(6) after the inner FACT(3) returns 6. The phrase double factorial refers only to the first operation.

Six distinct labeled objects A through F must be divided into three unordered pairs. Pair A with any of five other objects; four objects remain, giving three choices for the next smallest unused label; the last pair is forced.

=FACTDOUBLE(6-1)

Expected pairing count: 15, from 5×3×1. For eight objects, =FACTDOUBLE(8-1) gives 105. Reordering the pairs or swapping the order within a pair does not create a new pairing under this definition.

This is a combinatorial count, not a method for choosing an optimal matching. If pair order or an assigned first/second role matters, the outcome space changes and the simple pairing count no longer answers that question.

For n=4:

=FACTDOUBLE(2*4)
=2^4*FACT(4)

Both expected values are 384. Each of the four even factors contributes a factor of two, leaving 4×3×2×1 after those twos are removed.

For the odd product, =FACT(8)/(2^4*FACT(4)) gives 105, agreeing with FACTDOUBLE(7). These are useful independent checks at small sizes. They do not guarantee identical numerical stability for large inputs and large factorial intermediates.

Check whether the model uses an even or odd count, whether objects are distinguishable, and whether pairs themselves are ordered. The function cannot infer those assumptions.

The empty-product convention gives mathematical 0!!=1, but no newly executed zero-input Excel result is supplied here. Negative inputs and nonnumeric arguments have explicit vendor error rules; exact overflow limits and a full imported-type matrix remain outside this verification scope.

• Microsoft FACTDOUBLE reference.
• Editorial testing standards.

Worked inputs are fictional. Decimal answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.