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 A382800 #13 Apr 05 2025 16:09:57
%S A382800 1,0,0,0,3,0,0,3,3,0,0,6,27,6,0,0,18,78,78,18,0,0,72,282,588,282,72,0,
%T A382800 0,360,1272,2988,2988,1272,360,0,0,2160,6936,16344,24612,16344,6936,
%U A382800 2160,0,0,15120,44496,101448,175632,175632,101448,44496,15120,0
%N A382800 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))^3.
%F A382800 E.g.f.: 1 / (1 - log(1-x) * log(1-y))^3.
%F A382800 A(n,k) = A(k,n).
%F A382800 A(n,k) = Sum_{j=0..min(n,k)} (j!)^2 * binomial(j+2,2) * |Stirling1(n,j)| * |Stirling1(k,j)|.
%e A382800 Square array begins:
%e A382800 1, 0, 0, 0, 0, 0, ...
%e A382800 0, 3, 3, 6, 18, 72, ...
%e A382800 0, 3, 27, 78, 282, 1272, ...
%e A382800 0, 6, 78, 588, 2988, 16344, ...
%e A382800 0, 18, 282, 2988, 24612, 175632, ...
%e A382800 0, 72, 1272, 16344, 175632, 1669128, ...
%o A382800 (PARI) a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+2, 2)*abs(stirling(n, j, 1)*stirling(k, j, 1)));
%Y A382800 Main diagonal gives A382806.
%Y A382800 Cf. A379821, A382799.
%Y A382800 Cf. A382735, A382802.
%K A382800 nonn,tabl
%O A382800 0,5
%A A382800 _Seiichi Manyama_, Apr 05 2025