A174486 - OEIS

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

%S 1,1,5,70,1973,94216,6851197,706335064,98105431657,17669939141440,

%T 4006704580744601,1117139031649249984,375701872315954792093,

%U 149988716080978525265776,70129434038848683974552365

%N Column 0 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=0)=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, A174487, A174488, A174489.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Apr 18 2010