%I #2 Mar 30 2012 18:37:18
%S 1,2,9,78,1038,18968,443595,12681960,429244197,16801151910,
%T 746998729887,37200237947376,2051666003699226,124156748403386646,
%U 8180285024067867345,582970677419310149580,44684461723038752605932
%N Column 1 of triangle A166890.
%C Triangle A166890 transforms diagonals in the triangle A166888 of coefficients in the successive iterations of x*(1+x)^2.
%o (PARI) {a(n)=local(F=x, M, N, P, m=n); M=matrix(m+2, m+2, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, x+2*x^2+x^3+x*O(x^(m+2)))); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, M[r, c]); P=matrix(m+1, m+1, r, c, M[r+1, c]); (P~*N~^-1)[n, 1]}
%Y Cf. A166890, A166892, A166893.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Nov 22 2009