A382823 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y)) ).
1, 1, 1, 2, 2, 2, 6, 5, 5, 6, 24, 17, 17, 17, 24, 120, 74, 69, 69, 74, 120, 720, 394, 338, 337, 338, 394, 720, 5040, 2484, 1962, 1894, 1894, 1962, 2484, 5040, 40320, 18108, 13228, 12194, 12152, 12194, 13228, 18108, 40320, 362880, 149904, 101812, 89160, 87320, 87320, 89160, 101812, 149904, 362880
Offset: 0
Examples
Square array begins:
1, 1, 2, 6, 24, 120, ...
1, 2, 5, 17, 74, 394, ...
2, 5, 17, 69, 338, 1962, ...
6, 17, 69, 337, 1894, 12194, ...
24, 74, 338, 1894, 12152, 87320, ...
120, 394, 1962, 12194, 87320, 696076, ...
Crossrefs
Programs
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PARI
a(n, k) = sum(j=0, min(n, k), j!^2*abs(stirling(n+1, j+1, 1)*stirling(k+1, j+1, 1)));
Formula
E.g.f.: 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y)) ).
A(n,k) = A(k,n).
A(n,k) = Sum_{j=0..min(n,k)} (j!)^2 * |Stirling1(n+1,j+1)| * |Stirling1(k+1,j+1)|.