A174489 Column 3 of triangle A174485.

1, 4, 56, 1672, 85904, 6741544, 749040472, 111786940612, 21558649749088, 5215883627856592, 1546429233541304456, 551278120123210461436, 232603216443181020788944, 114634034948809175011787176

Offset: 0

Author

Paul D. Hanna, Apr 18 2010

Keywords

• nonn

Comments

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

Crossrefs

Cf. A174480, A174485, A174486, A174487, A174488.

Programs

PARI

{a(n,k=3)=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]}