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 A382734 #16 Apr 04 2025 10:20:43
%S A382734 1,0,0,0,2,0,0,2,2,0,0,2,14,2,0,0,2,38,38,2,0,0,2,86,254,86,2,0,0,2,
%T A382734 182,1118,1118,182,2,0,0,2,374,4142,8654,4142,374,2,0,0,2,758,14078,
%U A382734 51662,51662,14078,758,2,0,0,2,1526,45614,267566,467102,267566,45614,1526,2,0
%N A382734 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (exp(x) + exp(y) - exp(x+y))^2.
%F A382734 E.g.f.: 1 / (exp(x) + exp(y) - exp(x+y))^2.
%F A382734 A(n,k) = A(k,n).
%F A382734 A(n,k) = Sum_{j=0..min(n,k)} j! * (j+1)! * Stirling2(n,j) * Stirling2(k,j).
%e A382734 Square array begins:
%e A382734 1, 0, 0, 0, 0, 0, ...
%e A382734 0, 2, 2, 2, 2, 2, ...
%e A382734 0, 2, 14, 38, 86, 182, ...
%e A382734 0, 2, 38, 254, 1118, 4142, ...
%e A382734 0, 2, 86, 1118, 8654, 51662, ...
%e A382734 0, 2, 182, 4142, 51662, 467102, ...
%o A382734 (PARI) a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*stirling(n, j, 2)*stirling(k, j, 2));
%Y A382734 Main diagonal gives A382737.
%Y A382734 Cf. A371761, A382735, A382736.
%Y A382734 Cf. A136126, A382740.
%K A382734 nonn,tabl
%O A382734 0,5
%A A382734 _Seiichi Manyama_, Apr 04 2025