A364327 Number of endofunctions on [n] such that the number of elements that are mapped to i is either 0 or a divisor of i.

1, 1, 3, 13, 115, 851, 13431, 144516, 2782571, 47046307, 1107742273, 19263747713, 657152726011, 13657313316986, 451605697223110, 13377063396461138, 531234399267707419, 14563460779785318719, 721703507708044677945, 22141894282020163910406, 1123287408943765640907425

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Example

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).

Maple

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);

Crossrefs

Cf. A066843, A178682, A334370, A364328, A364344.

Sequence in context: A119723 A093011 A262147 * A057865 A344210 A260847

Adjacent sequences: A364324 A364325 A364326 * A364328 A364329 A364330

Keyword

nonn

Author

Alois P. Heinz, Jul 18 2023

Status

approved