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%I #2 Mar 30 2012 18:37:21
%S 1,4,36,1056,73200,9179640,1794887640,500614248960,187826632116480,
%T 90939137506660800,55080912083696452800,40741241351161144147200,
%U 36096696228114024645542400,37707879201499850798028974400
%N Column 1 of triangle A173210.
%C Triangle T = A173210 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, C=matrix(n+2,n+2,r,c,if(r==c,1,if(r==c+1,c)))); for(i=1, n+1, 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!); ); M[n+2,2]}
%Y Cf. A173210, A173211, A173213.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Feb 12 2010
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