cp's OEIS Frontend

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

%I A245507 #6 Jul 25 2014 11:41:37
%S A245507 1,1,3,19,73,901,1921,112015,87473,14154409,69703201,2929242031,
%T A245507 679876297,3090182325361,107695177409,442870698673621,
%U A245507 7233741446307841,475492243447425745,6964488144903745,672629401563923828521,2588222103446878841,615608908275758056730701
%N A245507 Number of endofunctions f on [n] such that f^n(i) = f(i) for all i in [n].
%H A245507 Alois P. Heinz, <a href="/A245507/b245507.txt">Table of n, a(n) for n = 0..150</a>
%F A245507 a(n) = n! * [x^n] exp(Sum_{d|(n-1)} (x*exp(x))^d/d) for n>1, a(0)=a(1)=1.
%F A245507 a(n) = A245501(n,n).
%p A245507 with(numtheory):
%p A245507 a:= n-> `if`(n<2, 1, n! *coeff(series(
%p A245507     exp(add((x*exp(x))^d/d, d=divisors(n-1))), x, n+1), x, n)):
%p A245507 seq(a(n), n=0..25);
%Y A245507 Main diagonal of A245501.
%K A245507 nonn
%O A245507 0,3
%A A245507 _Alois P. Heinz_, Jul 24 2014