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 A379821 #10 Apr 05 2025 16:09:40
%S A379821 1,0,0,0,1,0,0,1,1,0,0,2,5,2,0,0,6,14,14,6,0,0,24,50,76,50,24,0,0,120,
%T A379821 224,360,360,224,120,0,0,720,1216,1908,2392,1908,1216,720,0,0,5040,
%U A379821 7776,11628,15664,15664,11628,7776,5040,0
%N A379821 Array read by ascending antidiagonals: A(n, k) = (-1)^(n + k) * Sum_{j=0..k} (j!)^2 * Stirling1(n, j) * Stirling1(k, j).
%F A379821 E.g.f.: 1 / (1 - log(1-x) * log(1-y)). - _Seiichi Manyama_, Apr 05 2025
%e A379821 Array begins:
%e A379821 [0] 1, 0, 0, 0, 0, 0, 0, 0, ...
%e A379821 [1] 0, 1, 1, 2, 6, 24, 120, 720, ...
%e A379821 [2] 0, 1, 5, 14, 50, 224, 1216, 7776, ...
%e A379821 [3] 0, 2, 14, 76, 360, 1908, 11628, 81072, ...
%e A379821 [4] 0, 6, 50, 360, 2392, 15664, 110336, 856080, ...
%e A379821 [5] 0, 24, 224, 1908, 15664, 126676, 1046780, 9169920, ...
%e A379821 [6] 0, 120, 1216, 11628, 110336, 1046780, 10057204, 99846144, ...
%e A379821 .
%e A379821 Triangle T(n, k) = A(n - k, k) starts:
%e A379821 [0] 1;
%e A379821 [1] 0, 0;
%e A379821 [2] 0, 1, 0;
%e A379821 [3] 0, 1, 1, 0;
%e A379821 [4] 0, 2, 5, 2, 0;
%e A379821 [5] 0, 6, 14, 14, 6, 0;
%e A379821 [6] 0, 24, 50, 76, 50, 24, 0;
%e A379821 [7] 0, 120, 224, 360, 360, 224, 120, 0;
%e A379821 [8] 0, 720, 1216, 1908, 2392, 1908, 1216, 720, 0;
%p A379821 A := (n, k) -> local j; (-1)^(n + k)*add((j!)^2*Stirling1(n, j)*Stirling1(k, j), j = 0..k):
%p A379821 seq(lprint(seq(A(n, k), k = 0..7)), n = 0..8);
%o A379821 (PARI) a(n, k) = sum(j=0, min(n, k), j!^2*abs(stirling(n, j, 1)*stirling(k, j, 1))); \\ _Seiichi Manyama_, Apr 05 2025
%Y A379821 Main diagonal gives A382792.
%Y A379821 The corresponding array with Stirling2 numbers is A371761.
%K A379821 nonn,tabl
%O A379821 0,12
%A A379821 _Peter Luschny_, Jan 03 2025