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 A382825 #11 Apr 06 2025 08:46:30
%S A382825 1,1,1,2,4,2,6,11,11,6,24,39,55,39,24,120,174,255,255,174,120,720,942,
%T A382825 1338,1623,1338,942,720,5040,6012,8106,10434,10434,8106,6012,5040,
%U A382825 40320,44244,56292,72762,82116,72762,56292,44244,40320,362880,369072,442860,560988,668580,668580,560988,442860,369072,362880
%N A382825 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))^3 ).
%F A382825 E.g.f.: 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y))^3 ).
%F A382825 A(n,k) = A(k,n).
%F A382825 A(n,k) = Sum_{j=0..min(n,k)} (j!)^2 * binomial(j+2,2) * |Stirling1(n+1,j+1)| * |Stirling1(k+1,j+1)|.
%e A382825 Square array begins:
%e A382825 1, 1, 2, 6, 24, 120, ...
%e A382825 1, 4, 11, 39, 174, 942, ...
%e A382825 2, 11, 55, 255, 1338, 8106, ...
%e A382825 6, 39, 255, 1623, 10434, 72762, ...
%e A382825 24, 174, 1338, 10434, 82116, 668580, ...
%e A382825 120, 942, 8106, 72762, 668580, 6302028, ...
%o A382825 (PARI) a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+2, 2)*abs(stirling(n+1, j+1, 1)*stirling(k+1, j+1, 1)));
%Y A382825 Main diagonal gives A382828.
%Y A382825 Cf. A382823, A382824.
%Y A382825 Cf. A382673, A382800.
%K A382825 nonn,tabl
%O A382825 0,4
%A A382825 _Seiichi Manyama_, Apr 06 2025