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%I #2 Mar 30 2012 18:37:21
%S 0,4,18,672,51600,6883920,1399989780,401060653056,153389081849472,
%T 75336980135472000,46137556536570417600,34425740593629308436480,
%U 30717476677184291740437120,32275806213061043955592058880
%N Column 1 of triangle A173220.
%C Triangle A173220 is the matrix log of triangle T = A173210, which satisfies: row n of T^n = row n of (I+D)^(n^2) where D is the lower diagonal matrix: D(n+1,n)=n+1.
%o (PARI) {a(n)=local(M=Mat(1), N, L=Mat(1), C=matrix(n+3,n+3,r,c,if(r==c,1,if(r==c+1,c)))); for(i=1, n+2, N=M; M=matrix(#N+1, #N+1, r, c, if(r>=c, if(r<=#N, (N^(#N))[r, c], (C^((#M)^2))[r, c]))); L=sum(i=1, #M, -(M^0-M)^i/i); M=sum(i=0, #M, (L/#N)^i/i!); ); L[n+2, 2]/(n+2)}
%Y Cf. A173220, A173221, A173223, A173224.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Feb 12 2010
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