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 A382827 #8 Apr 06 2025 05:08:54
%S A382827 1,3,34,854,37556,2546852,246113904,32104625520,5433891955968,
%T A382827 1157778241057152,303197684900579712,95717977509042032256,
%U A382827 35847800701044816248064,15713483696924130220098816,7969364997624587289470810112,4630203661005094483980386924544
%N A382827 a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n+1,k+1)^2.
%F A382827 a(n) = (n!)^2 * [(x*y)^n] 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y))^2 ).
%F A382827 a(n) = (n!)^2 * [(x*y)^n] 1 / ( (1+x) * (1+y) * (1 - log(1+x) * log(1+y))^2 ).
%o A382827 (PARI) a(n) = sum(k=0, n, k!*(k+1)!*stirling(n+1, k+1, 1)^2);
%Y A382827 Main diagonal of A382824.
%Y A382827 Cf. A092552, A382804.
%K A382827 nonn
%O A382827 0,2
%A A382827 _Seiichi Manyama_, Apr 06 2025