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Column 0 of triangle A126465.
4

%I #3 Mar 30 2012 18:37:02

%S 1,1,3,33,855,40475,3039204,331630320,49563943161,9722245517970,

%T 2423526680920125,748560249534719259,280702726068079355157,

%U 125661789748507921799800,66215986172320048509110050

%N Column 0 of triangle A126465.

%o (PARI) {a(n)=local(M=matrix(n+1,n+1,r,c,if(r>=c,binomial((r-1)*r*(r+1)/3!-(c-1)*c*(c+1)/3!,r-c))), N=matrix(n+1,n+1,r,c,if(r>=c,binomial((r-1)*r*(r+1)/3!-(c-1)*c*(c+1)/3!+1,r-c)))); (N*M^-1)[n+1,1]}

%Y Cf. A126465, A126467, A126468; A126469 (row sums).

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 27 2006