A382734 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (exp(x) + exp(y) - exp(x+y))^2.
1, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 14, 2, 0, 0, 2, 38, 38, 2, 0, 0, 2, 86, 254, 86, 2, 0, 0, 2, 182, 1118, 1118, 182, 2, 0, 0, 2, 374, 4142, 8654, 4142, 374, 2, 0, 0, 2, 758, 14078, 51662, 51662, 14078, 758, 2, 0, 0, 2, 1526, 45614, 267566, 467102, 267566, 45614, 1526, 2, 0
Offset: 0
Examples
Square array begins: 1, 0, 0, 0, 0, 0, ... 0, 2, 2, 2, 2, 2, ... 0, 2, 14, 38, 86, 182, ... 0, 2, 38, 254, 1118, 4142, ... 0, 2, 86, 1118, 8654, 51662, ... 0, 2, 182, 4142, 51662, 467102, ...
Programs
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PARI
a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*stirling(n, j, 2)*stirling(k, j, 2));
Formula
E.g.f.: 1 / (exp(x) + exp(y) - exp(x+y))^2.
A(n,k) = A(k,n).
A(n,k) = Sum_{j=0..min(n,k)} j! * (j+1)! * Stirling2(n,j) * Stirling2(k,j).