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).
1, 1, 1, 1, 11, 1, 1, 31, 31, 1, 1, 71, 271, 71, 1, 1, 151, 1291, 1291, 151, 1, 1, 311, 4951, 12011, 4951, 311, 1, 1, 631, 17131, 78451, 78451, 17131, 631, 1, 1, 1271, 56071, 426971, 820351, 426971, 56071, 1271, 1, 1, 2551, 177691, 2093491, 6709651, 6709651, 2093491, 177691, 2551, 1
Offset: 1
Examples
Square array begins: 1, 1, 1, 1, 1, 1, ... 1, 11, 31, 71, 151, 311, ... 1, 31, 271, 1291, 4951, 17131, ... 1, 71, 1291, 12011, 78451, 426971, ... 1, 151, 4951, 78451, 820351, 6709651, ... 1, 311, 17131, 426971, 6709651, 79008011, ...
Programs
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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;
Formula
E.g.f.: (1/4) * (1 / (exp(x) + exp(y) - exp(x+y))^4 - 1).
A(n,k) = A(k,n).
A(n,k) = (1/4) * A382736(n,k).