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 A382793 #5 Apr 05 2025 10:24:32
%S A382793 1,-1,3,-1,-525,21599,-575757,-11712961,4147828275,-478419026401,
%T A382793 27474795508083,3849481231073279,-1772585499434165325,
%U A382793 366912253456842693599,-26525609280231515934477,-17189616925094873258825281,10414911263566240831226298675,-3136992122810471155294591778401
%N A382793 a(n) = Sum_{k=0..n} (-1)^k * (Stirling2(n,k) * k!)^2.
%F A382793 a(n) = (n!)^2 * [(x*y)^n] 1 / (2 - exp(x) - exp(y) + exp(x + y)).
%t A382793 Table[Sum[(-1)^k (StirlingS2[n, k] k!)^2, {k, 0, n}], {n, 0, 17}]
%t A382793 Table[(n!)^2 SeriesCoefficient[1/(2 - Exp[x] - Exp[y] + Exp[x + y]), {x, 0, n}, {y, 0, n}], {n, 0, 17}]
%Y A382793 Cf. A047797, A048144, A192552.
%K A382793 sign
%O A382793 0,3
%A A382793 _Ilya Gutkovskiy_, Apr 05 2025