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 A382735 #15 Apr 04 2025 09:19:54
%S A382735 1,0,0,0,3,0,0,3,3,0,0,3,27,3,0,0,3,75,75,3,0,0,3,171,579,171,3,0,0,3,
%T A382735 363,2667,2667,363,3,0,0,3,747,10083,22779,10083,747,3,0,0,3,1515,
%U A382735 34635,142923,142923,34635,1515,3,0,0,3,3051,112899,761211,1396803,761211,112899,3051,3,0
%N A382735 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))^3.
%F A382735 E.g.f.: 1 / (exp(x) + exp(y) - exp(x+y))^3.
%F A382735 A(n,k) = A(k,n).
%F A382735 A(n,k) = Sum_{j=0..min(n,k)} (j!)^2 * binomial(j+2,2) * Stirling2(n,j) * Stirling2(k,j).
%e A382735 Square array begins:
%e A382735 1, 0, 0, 0, 0, 0, ...
%e A382735 0, 3, 3, 3, 3, 3, ...
%e A382735 0, 3, 27, 75, 171, 363, ...
%e A382735 0, 3, 75, 579, 2667, 10083, ...
%e A382735 0, 3, 171, 2667, 22779, 142923, ...
%e A382735 0, 3, 363, 10083, 142923, 1396803, ...
%o A382735 (PARI) a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+2, 2)*stirling(n, j, 2)*stirling(k, j, 2));
%Y A382735 Main diagonal gives A382738.
%Y A382735 Cf. A371761, A382734, A382736.
%Y A382735 Cf. A382673, A382741.
%K A382735 nonn,tabl
%O A382735 0,5
%A A382735 _Seiichi Manyama_, Apr 04 2025