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 A382740 #12 Apr 04 2025 06:32:55 %S A382740 1,1,1,1,7,1,1,19,19,1,1,43,127,43,1,1,91,559,559,91,1,1,187,2071, %T A382740 4327,2071,187,1,1,379,7039,25831,25831,7039,379,1,1,763,22807,133783, %U A382740 233551,133783,22807,763,1,1,1531,71839,636679,1748791,1748791,636679,71839,1531,1 %N A382740 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/2) * (1 / (exp(x) + exp(y) - exp(x+y))^2 - 1). %F A382740 E.g.f.: (1/2) * (1 / (exp(x) + exp(y) - exp(x+y))^2 - 1). %F A382740 A(n,k) = A(k,n). %F A382740 A(n,k) = (1/2) * A382734(n,k). %e A382740 Square array begins: %e A382740 1, 1, 1, 1, 1, 1, ... %e A382740 1, 7, 19, 43, 91, 187, ... %e A382740 1, 19, 127, 559, 2071, 7039, ... %e A382740 1, 43, 559, 4327, 25831, 133783, ... %e A382740 1, 91, 2071, 25831, 233551, 1748791, ... %e A382740 1, 187, 7039, 133783, 1748791, 18207367, ... %o A382740 (PARI) a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*stirling(n, j, 2)*stirling(k, j, 2))/2; %Y A382740 Cf. A272644, A382741, A382742. %Y A382740 Cf. A382734. %K A382740 nonn,tabl %O A382740 1,5 %A A382740 _Seiichi Manyama_, Apr 04 2025