A174496 a(n) = coefficient of x^n/(n-1)! in the 6-fold iteration of x*exp(x).

1, 6, 66, 1041, 21216, 527631, 15441636, 518651881, 19630068656, 825581830491, 38159948599956, 1921319136589221, 104603652465885096, 6120324106269585751, 382829011514506048556, 25484466375276284094561

Offset: 1

Author

Paul D. Hanna, Apr 17 2010

Keywords

• nonn

Examples

			E.g.f.: x + 6*x^2 + 66*x^3/2! + 1041*x^4/3! + 21216*x^5/4! +...
		

Crossrefs

Cf. A174480, A080108, A174493, A174494, A174495.

Programs

PARI

{a(n)=local(F=x, xEx=x*exp(x+x*O(x^n))); for(i=1,6,F=subst(F, x, xEx));(n-1)!*polcoeff(F, n)}

Formula

O.g.f.: Sum_{n>=1} A174495(n)*x^n/(1-n*x)^n, where A174495(n) = [x^n/(n-1)! ] E(E(E(E(E(x))))) and E(x) = x*exp(x).

E.g.f. equals the 2-fold iteration of the e.g.f. of A174493.

E.g.f. equals the 3-fold iteration of the e.g.f. of A080108.