A245504 Number of endofunctions f on [n] such that f^8(i) = f(i) for all i in [n].

1, 1, 3, 10, 41, 196, 1057, 7042, 87473, 2004328, 50881121, 1200507694, 26179091017, 538344201292, 10635924720449, 204889902343666, 3902206399428833, 74966895289570768, 1511315984060460865, 34267718094037895638, 937490346932078590841, 30931366331911427839156

Offset: 0

Author

Alois P. Heinz, Jul 24 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Column k=8 of A245501.

Programs

Maple

egf:= exp(x*exp(x)+x^7*exp(x)^7/7):
a:= n-> n!*coeff(series(egf, x, n+1), x, n):
seq(a(n), n=0..25);

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x Exp[x]+(x^7 Exp[x]^7)/7],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 10 2016 *)

Formula

E.g.f.: exp(x*exp(x)+x^7*exp(x)^7/7).