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A275423 Number of set partitions of [n] such that five is a multiple of each block size. 2
1, 1, 1, 1, 1, 2, 7, 22, 57, 127, 379, 1849, 9109, 37324, 128129, 507508, 3031393, 19609773, 108440893, 500515633, 2467616641, 17154715726, 134519207131, 927764339426, 5359830269641, 31580724696907, 248587878630807, 2259650025239257, 18541914182165557 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..619

Wikipedia, Partition of a set

FORMULA

E.g.f.: exp(x+x^5/5!).

EXAMPLE

a(6) = 7: 12345|6, 12346|5, 12356|4, 12456|3, 13456|2, 1|23456, 1|2|3|4|5|6.

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(

      `if`(j>n, 0, a(n-j)*binomial(n-1, j-1)), j=[1, 5]))

    end:

seq(a(n), n=0..30);

MATHEMATICA

a[n_] := a[n] = If[n == 0, 1, Sum[If[j > n, 0, a[n-j]*Binomial[n-1, j-1]], {j, {1, 5}}]];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, May 17 2018, translated from Maple *)

CROSSREFS

Column k=5 of A275422.

Sequence in context: A099132 A139398 A226910 * A099131 A212384 A063019

Adjacent sequences:  A275420 A275421 A275422 * A275424 A275425 A275426

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 27 2016

STATUS

approved

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Last modified November 18 01:20 EST 2018. Contains 317279 sequences. (Running on oeis4.)