A364328 Number of endofunctions on [n] such that the number of elements that are mapped to i is either 0 or a prime divisor of i.

1, 0, 1, 1, 6, 21, 110, 904, 4312, 74400, 731412, 5600761, 128196024, 792051157, 18696610816, 264267572121, 7136433698464, 57948743342529, 2228312959187256, 22463157401776612, 681974906329502904, 15395459281239915282, 463374873030990445252, 6091833036158810701465

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..444

Example

a(0) = 1: ().
a(2) = 1: (22).
a(3) = 1: (333).
a(4) = 6: (4422), (4242), (4224), (2442), (2424), (2244).
a(5) = 21: (55555), (44333), (43433), (43343), (43334), (34433), (34343), (34334), (33443), (33434), (33344), (33322), (33232), (33223), (32332), (32323), (32233), (23332), (23323), (23233), (22333).

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[factorset](i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..23);

Crossrefs

Cf. A000040, A178682, A334370, A364327, A364344.

Sequence in context: A060843 A026650 A347948 * A298837 A009253 A365880

Adjacent sequences: A364325 A364326 A364327 * A364329 A364330 A364331

Keyword

nonn

Author

Alois P. Heinz, Jul 18 2023

Status

approved