A382824 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))^2 ).
1, 1, 1, 2, 3, 2, 6, 8, 8, 6, 24, 28, 34, 28, 24, 120, 124, 150, 150, 124, 120, 720, 668, 768, 854, 768, 668, 720, 5040, 4248, 4584, 5204, 5204, 4584, 4248, 5040, 40320, 31176, 31512, 35188, 37556, 35188, 31512, 31176, 40320, 362880, 259488, 246072, 265896, 290380, 290380, 265896, 246072, 259488, 362880
Offset: 0
Examples
Square array begins:
1, 1, 2, 6, 24, 120, ...
1, 3, 8, 28, 124, 668, ...
2, 8, 34, 150, 768, 4584, ...
6, 28, 150, 854, 5204, 35188, ...
24, 124, 768, 5204, 37556, 290380, ...
120, 668, 4584, 35188, 290380, 2546852, ...
Programs
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PARI
a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*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))^2 ).
A(n,k) = A(k,n).
A(n,k) = Sum_{j=0..min(n,k)} j! * (j+1)! * |Stirling1(n+1,j+1)| * |Stirling1(k+1,j+1)|.