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 A382741 #10 Apr 04 2025 06:31:21 %S A382741 1,1,1,1,9,1,1,25,25,1,1,57,193,57,1,1,121,889,889,121,1,1,249,3361, %T A382741 7593,3361,249,1,1,505,11545,47641,47641,11545,505,1,1,1017,37633, %U A382741 253737,465601,253737,37633,1017,1,1,2041,118969,1228249,3657721,3657721,1228249,118969,2041,1 %N A382741 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 / (exp(x) + exp(y) - exp(x+y))^3 - 1). %F A382741 E.g.f.: (1/3) * (1 / (exp(x) + exp(y) - exp(x+y))^3 - 1). %F A382741 A(n,k) = A(k,n). %F A382741 A(n,k) = (1/3) * A382735(n,k). %e A382741 Square array begins: %e A382741 1, 1, 1, 1, 1, 1, ... %e A382741 1, 9, 25, 57, 121, 249, ... %e A382741 1, 25, 193, 889, 3361, 11545, ... %e A382741 1, 57, 889, 7593, 47641, 253737, ... %e A382741 1, 121, 3361, 47641, 465601, 3657721, ... %e A382741 1, 249, 11545, 253737, 3657721, 40666089, ... %o A382741 (PARI) a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+2, 2)*stirling(n, j, 2)*stirling(k, j, 2))/3; %Y A382741 Cf. A272644, A382740, A382742. %Y A382741 Cf. A382735. %K A382741 nonn,tabl %O A382741 1,5 %A A382741 _Seiichi Manyama_, Apr 04 2025