A275429 Number of set partitions of [n] such that n is a multiple of each block size.

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

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-François Alcover, May 17 2018, translated from Maple *)

Crossrefs

Main diagonal of A275422.

Sequence in context: A141651 A359425 A213990 * A222878 A090525 A328455

Adjacent sequences: A275426 A275427 A275428 * A275430 A275431 A275432

Keyword

nonn

Author

Alois P. Heinz, Jul 27 2016

Status

approved