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 A382742 #10 Apr 04 2025 06:31:14 %S A382742 1,1,1,1,11,1,1,31,31,1,1,71,271,71,1,1,151,1291,1291,151,1,1,311, %T A382742 4951,12011,4951,311,1,1,631,17131,78451,78451,17131,631,1,1,1271, %U A382742 56071,426971,820351,426971,56071,1271,1,1,2551,177691,2093491,6709651,6709651,2093491,177691,2551,1 %N A382742 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/4) * (1 / (exp(x) + exp(y) - exp(x+y))^4 - 1). %F A382742 E.g.f.: (1/4) * (1 / (exp(x) + exp(y) - exp(x+y))^4 - 1). %F A382742 A(n,k) = A(k,n). %F A382742 A(n,k) = (1/4) * A382736(n,k). %e A382742 Square array begins: %e A382742 1, 1, 1, 1, 1, 1, ... %e A382742 1, 11, 31, 71, 151, 311, ... %e A382742 1, 31, 271, 1291, 4951, 17131, ... %e A382742 1, 71, 1291, 12011, 78451, 426971, ... %e A382742 1, 151, 4951, 78451, 820351, 6709651, ... %e A382742 1, 311, 17131, 426971, 6709651, 79008011, ... %o A382742 (PARI) a(n, k) = sum(j=0, min(n, k), j!^2*binomial(j+3, 3)*stirling(n, j, 2)*stirling(k, j, 2))/4; %Y A382742 Cf. A272644, A382740, A382741. %Y A382742 Cf. A382736. %K A382742 nonn,tabl %O A382742 1,5 %A A382742 _Seiichi Manyama_, Apr 04 2025