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 A382824 #12 Apr 06 2025 08:46:34
%S A382824 1,1,1,2,3,2,6,8,8,6,24,28,34,28,24,120,124,150,150,124,120,720,668,
%T A382824 768,854,768,668,720,5040,4248,4584,5204,5204,4584,4248,5040,40320,
%U A382824 31176,31512,35188,37556,35188,31512,31176,40320,362880,259488,246072,265896,290380,290380,265896,246072,259488,362880
%N A382824 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y))^2 ).
%F A382824 E.g.f.: 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y))^2 ).
%F A382824 A(n,k) = A(k,n).
%F A382824 A(n,k) = Sum_{j=0..min(n,k)} j! * (j+1)! * |Stirling1(n+1,j+1)| * |Stirling1(k+1,j+1)|.
%e A382824 Square array begins:
%e A382824 1, 1, 2, 6, 24, 120, ...
%e A382824 1, 3, 8, 28, 124, 668, ...
%e A382824 2, 8, 34, 150, 768, 4584, ...
%e A382824 6, 28, 150, 854, 5204, 35188, ...
%e A382824 24, 124, 768, 5204, 37556, 290380, ...
%e A382824 120, 668, 4584, 35188, 290380, 2546852, ...
%o A382824 (PARI) a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*abs(stirling(n+1, j+1, 1)*stirling(k+1, j+1, 1)));
%Y A382824 Main diagonal gives A382827.
%Y A382824 Cf. A382823, A382825.
%K A382824 nonn,tabl
%O A382824 0,4
%A A382824 _Seiichi Manyama_, Apr 05 2025