A382801 - OEIS

%I #14 Apr 05 2025 23:17:14

%S 1,1,1,2,7,2,6,20,20,6,24,72,130,72,24,120,324,642,642,324,120,720,

%T 1764,3468,4794,3468,1764,720,5040,11304,21372,32964,32964,21372,

%U 11304,5040,40320,83448,150120,238404,290976,238404,150120,83448,40320

%N Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/2) * (1 / (1 - log(1-x) * log(1-y))^2 - 1).

%F E.g.f.: (1/2) * (1 / (1 - log(1-x) * log(1-y))^2 - 1).

%F A(n,k) = A(k,n).

%F A(n,k) = (1/2) * A382799(n,k).

%e Square array begins:

%e     1,    1,     2,      6,      24,      120, ...

%e     1,    7,    20,     72,     324,     1764, ...

%e     2,   20,   130,    642,    3468,    21372, ...

%e     6,   72,   642,   4794,   32964,   238404, ...

%e    24,  324,  3468,  32964,  290976,  2524080, ...

%e   120, 1764, 21372, 238404, 2524080, 26048256, ...

%o (PARI) a(n, k) = sum(j=0, min(n, k), j!*(j+1)!*abs(stirling(n, j, 1)*stirling(k, j, 1)))/2;

%Y Cf. A382740, A382799.

%K nonn,tabl

%O 1,4

%A _Seiichi Manyama_, Apr 05 2025