A060907 - OEIS

%I #13 Jul 25 2014 09:40:27

%S 1,1,4,19,116,901,8422,89755,1061048,13746169,193901066,2965146559,

%T 48946004956,867463969789,16405240966766,329147315037811,

%U 6973157545554128,155446026607476145,3636697161715448914,89099916704329731895,2281451214192505136516

%N E.g.f.: exp(x*exp(x) + 1/2*x^2*exp(x)^2 + 1/4*x^4*exp(x)^4).

%C The number of functions from {1,2,...,n} into itself such that f(x) = f^5(x). - _Geoffrey Critzer_, Sep 18 2012

%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.

%H Alois P. Heinz, <a href="/A060907/b060907.txt">Table of n, a(n) for n = 0..200</a>

%F E.g.f.: exp(Sum_{d|m} T_k^d/d), where T_k = x*exp(T_(k - 1)), k >= 1, T_0 = x; k = 1, m = 4.

%p egf:= exp(x*exp(x)+x^2*exp(x)^2/2+x^4*exp(x)^4/4):

%p a:= n-> n!*coeff(series(egf, x, n+11), x, n):

%p seq(a(n), n=0..25);  # _Alois P. Heinz_, Jul 25 2014

%t nn=20;a=x Exp[x];Range[0,nn]!CoefficientList[Series[Exp[a+a^2/2+a^4/4],{x,0,nn}],x] (* _Geoffrey Critzer_, Sep 18 2012 *)

%Y Cf. A000949 - A000951, A060905 - A060913.

%Y Column k=5 of A245501.

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Apr 07 2001