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A245507
Number of endofunctions f on [n] such that f^n(i) = f(i) for all i in [n].
2
1, 1, 3, 19, 73, 901, 1921, 112015, 87473, 14154409, 69703201, 2929242031, 679876297, 3090182325361, 107695177409, 442870698673621, 7233741446307841, 475492243447425745, 6964488144903745, 672629401563923828521, 2588222103446878841, 615608908275758056730701
OFFSET
0,3
LINKS
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).
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);
CROSSREFS
Main diagonal of A245501.
Sequence in context: A350713 A215802 A202041 * A247059 A243142 A174286
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 24 2014
STATUS
approved