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 A382792 #16 Apr 05 2025 16:09:44
%S A382792 1,1,5,76,2392,126676,10057204,1114096320,163918005696,30894047577216,
%T A382792 7254176241285504,2075722128162164736,710883208780304954112,
%U A382792 287061726161439955116288,134961239570613490548986112,73079781978184515947237031936,45150931601954398539342470578176
%N A382792 a(n) = Sum_{k=0..n} (Stirling1(n,k) * k!)^2.
%C A382792 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 A382792 a(n) = (n!)^2 * [(x*y)^n] 1 / (1 - log(1 + x) * log(1 + y)).
%F A382792 a(n) = (n!)^2 * [(x*y)^n] 1 / (1 - log(1 - x) * log(1 - y)).
%F A382792 a(n) ~ sqrt(Pi) * n^(2*n + 1/2) / (exp(1) - 1)^(2*n+1). - _Vaclav Kotesovec_, Apr 05 2025
%t A382792 Table[Sum[(StirlingS1[n, k] k!)^2, {k, 0, n}], {n, 0, 16}]
%t A382792 Table[(n!)^2 SeriesCoefficient[1/(1 - Log[1 + x] Log[1 + y]), {x, 0, n}, {y, 0, n}], {n, 0, 16}]
%o A382792 (PARI) a(n) = sum(k=0, n, (k!*stirling(n, k, 1))^2); \\ _Seiichi Manyama_, Apr 05 2025
%Y A382792 Main diagonal of A379821.
%Y A382792 Cf. A006252, A007840, A047796, A048144, A382794.
%K A382792 nonn
%O A382792 0,3
%A A382792 _Ilya Gutkovskiy_, Apr 05 2025