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A275429 Number of set partitions of [n] such that n is a multiple of each block size. 4
1, 1, 2, 2, 11, 2, 167, 2, 1500, 1206, 16175, 2, 3486584, 2, 3188421, 29226654, 772458367, 2, 130880325103, 2, 4173951684174, 623240762412, 644066092301, 2, 220076136813712815, 31580724696908, 538897996103277, 49207275464475052, 44147498142028751570, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..587

Wikipedia, Partition of a set

FORMULA

a(n) = n! * [x^n] exp(Sum_{d|n} x^d/d!) for n>0, a(0) = 1.

a(n) = A275422(n,n).

a(p) = 2 for p prime.

EXAMPLE

a(4) = 11: 1234, 12|34, 12|3|4, 13|24, 13|2|4, 14|23, 1|23|4, 14|2|3, 1|24|3, 1|2|34, 1|2|3|4.

a(5) = 2: 12345, 1|2|3|4|5.

MAPLE

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

      `if`(j>n, 0, A(n-j, k)*binomial(n-1, j-1)), j=

      `if`(k=0, 1..n, numtheory[divisors](k))))

    end:

a:= n-> A(n$2):

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

MATHEMATICA

A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[If[j > n, 0, A[n - j, k]* Binomial[n - 1, j - 1]], {j, If[k == 0, Range[n], Divisors[k]]}]];

a[n_] := A[n, n];

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

CROSSREFS

Main diagonal of A275422.

Sequence in context: A037234 A141651 A213990 * A222878 A090525 A328455

Adjacent sequences:  A275426 A275427 A275428 * A275430 A275431 A275432

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 27 2016

STATUS

approved

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Last modified May 27 01:35 EDT 2022. Contains 354092 sequences. (Running on oeis4.)