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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. 3
1, 0, 1, 1, 6, 21, 110, 904, 4312, 74400, 731412, 5600761, 128196024, 792051157, 18696610816, 264267572121, 7136433698464, 57948743342529, 2228312959187256, 22463157401776612, 681974906329502904, 15395459281239915282, 463374873030990445252, 6091833036158810701465 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
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
Sequence in context: A060843 A026650 A347948 * A298837 A009253 A365880
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 18 2023
STATUS
approved

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Last modified June 17 06:37 EDT 2024. Contains 373432 sequences. (Running on oeis4.)