This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382808 #7 Apr 06 2025 05:52:03
%S A382808 1,1,9,440,71344,25826824,17321581592,19304140340736,
%T A382808 33142988156751360,82906630912116006912,289508760665893747703808,
%U A382808 1364207202603804952193826816,8438589244471363680258331914240,66972265137135031645961782287814656,668922701586813036491303458870218731520
%N A382808 a(n) = Sum_{k=0..n} (|Stirling1(n,k)| * k!)^3.
%C A382808 In general, for m>=1, Sum_{k=0..n} (abs(Stirling1(n,k)) * k!)^m ~ sqrt(2*Pi/m) * n^(m*n + 1/2) / (exp(1) - 1)^(m*n+1). - _Vaclav Kotesovec_, Apr 05 2025
%F A382808 a(n) = (n!)^3 * [(x*y*z)^n] 1 / (1 + log(1 - x) * log(1 - y) * log(1 - z)).
%F A382808 a(n) ~ sqrt(2*Pi/3) * n^(3*n + 1/2) / (exp(1) - 1)^(3*n+1). - _Vaclav Kotesovec_, Apr 05 2025
%t A382808 Table[Sum[(Abs[StirlingS1[n, k]] k!)^3, {k, 0, n}], {n, 0, 14}]
%t A382808 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}]
%Y A382808 Cf. A007840, A242280, A382792, A382807.
%K A382808 nonn
%O A382808 0,3
%A A382808 _Ilya Gutkovskiy_, Apr 05 2025