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 A382801 #14 Apr 05 2025 23:17:14 %S A382801 1,1,1,2,7,2,6,20,20,6,24,72,130,72,24,120,324,642,642,324,120,720, %T A382801 1764,3468,4794,3468,1764,720,5040,11304,21372,32964,32964,21372, %U A382801 11304,5040,40320,83448,150120,238404,290976,238404,150120,83448,40320 %N A382801 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/2) * (1 / (1 - log(1-x) * log(1-y))^2 - 1). %F A382801 E.g.f.: (1/2) * (1 / (1 - log(1-x) * log(1-y))^2 - 1). %F A382801 A(n,k) = A(k,n). %F A382801 A(n,k) = (1/2) * A382799(n,k). %e A382801 Square array begins: %e A382801 1, 1, 2, 6, 24, 120, ... %e A382801 1, 7, 20, 72, 324, 1764, ... %e A382801 2, 20, 130, 642, 3468, 21372, ... %e A382801 6, 72, 642, 4794, 32964, 238404, ... %e A382801 24, 324, 3468, 32964, 290976, 2524080, ... %e A382801 120, 1764, 21372, 238404, 2524080, 26048256, ... %o A382801 (PARI) a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*abs(stirling(n, j, 1)*stirling(k, j, 1)))/2; %Y A382801 Cf. A382740, A382799. %K A382801 nonn,tabl %O A382801 1,4 %A A382801 _Seiichi Manyama_, Apr 05 2025