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

Author

Alois P. Heinz, Jul 18 2023

Keywords

• nonn

Examples

			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).
		

Links

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

Crossrefs

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

Programs

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);