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A364327
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Number of endofunctions on [n] such that the number of elements that are mapped to i is either 0 or a divisor of i.
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3
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1, 1, 3, 13, 115, 851, 13431, 144516, 2782571, 47046307, 1107742273, 19263747713, 657152726011, 13657313316986, 451605697223110, 13377063396461138, 531234399267707419, 14563460779785318719, 721703507708044677945, 22141894282020163910406, 1123287408943765640907425
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(0) = 1: ().
a(1) = 1: (1).
a(2) = 3: (22), (21), (12).
a(3) = 13: (333), (322), (232), (223), (321), (231), (213), (312), (132), (123), (221), (212), (122).
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1)+add(
`if`(d>n, 0, b(n-d, i-1)*binomial(n, d)), d=numtheory[divisors](i))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..23);
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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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