A245507 Number of endofunctions f on [n] such that f^n(i) = f(i) for all i in [n].

1, 1, 3, 19, 73, 901, 1921, 112015, 87473, 14154409, 69703201, 2929242031, 679876297, 3090182325361, 107695177409, 442870698673621, 7233741446307841, 475492243447425745, 6964488144903745, 672629401563923828521, 2588222103446878841, 615608908275758056730701

Offset: 0

Author

Alois P. Heinz, Jul 24 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Main diagonal of A245501.

Programs

Maple

with(numtheory):
a:= n-> `if`(n<2, 1, n! *coeff(series(
    exp(add((x*exp(x))^d/d, d=divisors(n-1))), x, n+1), x, n)):
seq(a(n), n=0..25);

Formula

a(n) = n! * [x^n] exp(Sum_{d|(n-1)} (x*exp(x))^d/d) for n>1, a(0)=a(1)=1.

a(n) = A245501(n,n).