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%I #4 Jun 14 2017 00:39:20
%S 1,3,12,75,744,11181,242835,7330930,297801232,15839503630,
%T 1077837497949,92001213821228,9684980747377593,1239048275916503276,
%U 190191205778008667316,34634317805556075695994
%N Column 1 of triangle T=A134523, also equals column 0 of the matrix power T^3, where column k of T = column 0 of matrix power T^{(k+1)(k+2)/2} for k>=0.
%o (PARI) a(n)=local(A, B); A=matrix(1, 1); A[1, 1]=1; for(m=2, n+2, B=matrix(m, m); for(i=1, m, for(j=1, i, if(i<3 || j==i || j>m-1, B[i, j]=1, if(j==1, B[i, 1]=1, B[i, j]=(A^(j*(j+1)/2))[i-j+1, 1])); )); A=B); A[n+2, 2]
%Y Cf. A134523 (triangle); other columns: A134525, A134526.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 15 2007
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