A174488 - OEIS

%I #2 Mar 30 2012 18:37:21

%S 1,3,33,810,35325,2408568,236624733,31654735416,5532363865977,

%T 1223887080470256,334272773792556369,110467177430468340408,

%U 43442224822360939240629,20048090531903711663566248

%N Column 2 of triangle A174485.

%C Triangular matrix described by A174485 transforms diagonals of the array A174480 of coefficients of successive iterations of x*exp(x).

%o (PARI) {a(n,k=2)=local(F=x, xEx=x*exp(x+x*O(x^(n+k+1))), M, N, P, m=n+k); M=matrix(m+2, m+2, r, c, F=x; for(i=1, r+c-2, F=subst(F, x, xEx)); 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]); n!*(P~*N~^-1)[n+k+1, k+1]}

%Y Cf. A174480, A174485, A174486, A174487, A174489.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 18 2010