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 A382736 #16 Apr 04 2025 10:20:37
%S A382736 1,0,0,0,4,0,0,4,4,0,0,4,44,4,0,0,4,124,124,4,0,0,4,284,1084,284,4,0,
%T A382736 0,4,604,5164,5164,604,4,0,0,4,1244,19804,48044,19804,1244,4,0,0,4,
%U A382736 2524,68524,313804,313804,68524,2524,4,0,0,4,5084,224284,1707884,3281404,1707884,224284,5084,4,0
%N A382736 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))^4.
%F A382736 E.g.f.: 1 / (exp(x) + exp(y) - exp(x+y))^4.
%F A382736 A(n,k) = A(k,n).
%F A382736 A(n,k) = Sum_{j=0..min(n,k)} (j!)^2 * binomial(j+3,3) * Stirling2(n,j) * Stirling2(k,j).
%e A382736 Square array begins:
%e A382736 1, 0, 0, 0, 0, 0, ...
%e A382736 0, 4, 4, 4, 4, 4, ...
%e A382736 0, 4, 44, 124, 284, 604, ...
%e A382736 0, 4, 124, 1084, 5164, 19804, ...
%e A382736 0, 4, 284, 5164, 48044, 313804, ...
%e A382736 0, 4, 604, 19804, 313804, 3281404, ...
%o A382736 (PARI) a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+3, 3)*stirling(n, j, 2)*stirling(k, j, 2));
%Y A382736 Main diagonal gives A382739.
%Y A382736 Cf. A371761, A382734, A382735.
%Y A382736 Cf. A382674, A382742.
%K A382736 nonn,tabl
%O A382736 0,5
%A A382736 _Seiichi Manyama_, Apr 04 2025