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A275425 Number of set partitions of [n] such that seven is a multiple of each block size. 2
1, 1, 1, 1, 1, 1, 1, 2, 9, 37, 121, 331, 793, 1717, 5149, 32176, 217361, 1186329, 5282785, 20004037, 66589681, 266164921, 2012163385, 18230119678, 137986473241, 849028203101, 4391743155801, 19722685412431, 98510163677641, 856572597342541, 9516244046786101 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..618

Wikipedia, Partition of a set

FORMULA

E.g.f.: exp(x+x^7/7!).

EXAMPLE

a(8) = 9: 1234567|8, 1234568|7, 1234578|6, 1234678|5, 1235678|4, 1245678|3, 1345678|2, 1|2345678, 1|2|3|4|5|6|7|8.

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, 7]))

    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, 7}}]];

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

CROSSREFS

Column k=7 of A275422.

Sequence in context: A101610 A111601 A280351 * A212386 A206374 A037553

Adjacent sequences:  A275422 A275423 A275424 * A275426 A275427 A275428

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 27 2016

STATUS

approved

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Last modified December 17 02:29 EST 2018. Contains 318192 sequences. (Running on oeis4.)