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 A382823 #17 Apr 06 2025 03:48:25
%S A382823 1,1,1,2,2,2,6,5,5,6,24,17,17,17,24,120,74,69,69,74,120,720,394,338,
%T A382823 337,338,394,720,5040,2484,1962,1894,1894,1962,2484,5040,40320,18108,
%U A382823 13228,12194,12152,12194,13228,18108,40320,362880,149904,101812,89160,87320,87320,89160,101812,149904,362880
%N A382823 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-x) * (1-y) * (1 - log(1-x) * log(1-y)) ).
%F A382823 E.g.f.: 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y)) ).
%F A382823 A(n,k) = A(k,n).
%F A382823 A(n,k) = Sum_{j=0..min(n,k)} (j!)^2 * |Stirling1(n+1,j+1)| * |Stirling1(k+1,j+1)|.
%e A382823 Square array begins:
%e A382823 1, 1, 2, 6, 24, 120, ...
%e A382823 1, 2, 5, 17, 74, 394, ...
%e A382823 2, 5, 17, 69, 338, 1962, ...
%e A382823 6, 17, 69, 337, 1894, 12194, ...
%e A382823 24, 74, 338, 1894, 12152, 87320, ...
%e A382823 120, 394, 1962, 12194, 87320, 696076, ...
%o A382823 (PARI) a(n, k) = sum(j=0, min(n, k), j!^2*abs(stirling(n+1, j+1, 1)*stirling(k+1, j+1, 1)));
%Y A382823 Columns k=0..1 give A000142, A000774.
%Y A382823 Main diagonal gives A382826.
%Y A382823 Cf. A382824, A382825.
%Y A382823 Cf. A099594, A379821.
%K A382823 nonn,tabl
%O A382823 0,4
%A A382823 _Seiichi Manyama_, Apr 05 2025