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 A382799 #12 Apr 05 2025 16:10:01
%S A382799 1,0,0,0,2,0,0,2,2,0,0,4,14,4,0,0,12,40,40,12,0,0,48,144,260,144,48,0,
%T A382799 0,240,648,1284,1284,648,240,0,0,1440,3528,6936,9588,6936,3528,1440,0,
%U A382799 0,10080,22608,42744,65928,65928,42744,22608,10080,0,0,80640,166896,300240,476808,581952,476808,300240,166896,80640,0
%N A382799 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 - log(1-x) * log(1-y))^2.
%F A382799 E.g.f.: 1 / (1 - log(1-x) * log(1-y))^2.
%F A382799 A(n,k) = A(k,n).
%F A382799 A(n,k) = Sum_{j=0..min(n,k)} j! * (j+1)! * |Stirling1(n,j)| * |Stirling1(k,j)|.
%e A382799 Square array begins:
%e A382799 1, 0, 0, 0, 0, 0, ...
%e A382799 0, 2, 2, 4, 12, 48, ...
%e A382799 0, 2, 14, 40, 144, 648, ...
%e A382799 0, 4, 40, 260, 1284, 6936, ...
%e A382799 0, 12, 144, 1284, 9588, 65928, ...
%e A382799 0, 48, 648, 6936, 65928, 581952, ...
%o A382799 (PARI) a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*abs(stirling(n, j, 1)*stirling(k, j, 1)));
%Y A382799 Main diagonal gives A382804.
%Y A382799 Cf. A379821, A382800.
%Y A382799 Cf. A382734, A382801.
%K A382799 nonn,tabl
%O A382799 0,5
%A A382799 _Seiichi Manyama_, Apr 05 2025