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A245507
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Number of endofunctions f on [n] such that f^n(i) = f(i) for all i in [n].
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2
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1, 1, 3, 19, 73, 901, 1921, 112015, 87473, 14154409, 69703201, 2929242031, 679876297, 3090182325361, 107695177409, 442870698673621, 7233741446307841, 475492243447425745, 6964488144903745, 672629401563923828521, 2588222103446878841, 615608908275758056730701
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = n! * [x^n] exp(Sum_{d|(n-1)} (x*exp(x))^d/d) for n>1, a(0)=a(1)=1.
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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