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 A382802 #16 Apr 05 2025 23:17:20 %S A382802 1,1,1,2,9,2,6,26,26,6,24,94,196,94,24,120,424,996,996,424,120,720, %T A382802 2312,5448,8204,5448,2312,720,5040,14832,33816,58544,58544,33816, %U A382802 14832,5040,40320,109584,238656,431632,556376,431632,238656,109584,40320 %N A382802 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/3) * (1 / (1 - log(1-x) * log(1-y))^3 - 1). %F A382802 E.g.f.: (1/3) * (1 / (1 - log(1-x) * log(1-y))^3 - 1). %F A382802 A(n,k) = A(k,n). %F A382802 A(n,k) = (1/3) * A382800(n,k). %e A382802 Square array begins: %e A382802 1, 1, 2, 6, 24, 120, ... %e A382802 1, 9, 26, 94, 424, 2312, ... %e A382802 2, 26, 196, 996, 5448, 33816, ... %e A382802 6, 94, 996, 8204, 58544, 431632, ... %e A382802 24, 424, 5448, 58544, 556376, 5017480, ... %e A382802 120, 2312, 33816, 431632, 5017480, 55016408, ... %o A382802 (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)))/3; %Y A382802 Cf. A382741, A382800. %K A382802 nonn,tabl %O A382802 1,4 %A A382802 _Seiichi Manyama_, Apr 05 2025