A382808 a(n) = Sum_{k=0..n} (|Stirling1(n,k)| * k!)^3.
1, 1, 9, 440, 71344, 25826824, 17321581592, 19304140340736, 33142988156751360, 82906630912116006912, 289508760665893747703808, 1364207202603804952193826816, 8438589244471363680258331914240, 66972265137135031645961782287814656, 668922701586813036491303458870218731520
Offset: 0
Keywords
Programs
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Mathematica
Table[Sum[(Abs[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)).
a(n) ~ sqrt(2*Pi/3) * n^(3*n + 1/2) / (exp(1) - 1)^(3*n+1). - Vaclav Kotesovec, Apr 05 2025
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