A382807 a(n) = Sum_{k=0..n} (Stirling1(n,k) * k!)^3.

1, 1, 7, 8, -22400, -3821176, 733375592, 1324952888832, 521577465629184, -1322687167356985344, -3493561791052460040192, 83811280007607865122816, 33603928402796871413168222208, 112696506862115060894313558528000, -389416384673353674591900391305326592

Offset: 0

Author

Ilya Gutkovskiy, Apr 05 2025

Keywords

• sign

Crossrefs

Cf. A006252, A242280, A382792, A382808.

Programs

Mathematica

Table[Sum[(StirlingS1[n, k] k!)^3, {k, 0, n}], {n, 0, 14}]
Table[(n!)^3 SeriesCoefficient[1/(1 - Log[1 + x] Log[1 + y] Log[1 + z]), {x, 0, n}, {y, 0, n}, {z, 0, n}], {n, 0, 14}]

Formula

a(n) = (n!)^3 * [(x*y*z)^n] 1 / (1 - log(1 + x) * log(1 + y) * log(1 + z)).