|
%I #2 Mar 30 2012 18:37:21
%S 1,6,66,1041,21216,527631,15441636,518651881,19630068656,825581830491,
%T 38159948599956,1921319136589221,104603652465885096,
%U 6120324106269585751,382829011514506048556,25484466375276284094561
%N a(n) = coefficient of x^n/(n-1)! in the 6-fold iteration of x*exp(x).
%F 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).
%F E.g.f. equals the 2-fold iteration of the e.g.f. of A174493.
%F E.g.f. equals the 3-fold iteration of the e.g.f. of A080108.
%e E.g.f.: x + 6*x^2 + 66*x^3/2! + 1041*x^4/3! + 21216*x^5/4! +...
%o (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)}
%Y Cf. A174480, A080108, A174493, A174494, A174495.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Apr 17 2010
|
