A305551 Number of partitions of partitions of n where all partitions have the same sum.

1, 1, 3, 4, 9, 8, 22, 16, 43, 41, 77, 57, 201, 102, 264, 282, 564, 298, 1175, 491, 1878, 1509, 2611, 1256, 7872, 2421, 7602, 8026, 16304, 4566, 38434, 6843, 48308, 41078, 56582, 28228, 221115, 21638, 146331, 208142, 453017, 44584, 844773, 63262, 1034193, 1296708

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{d|n} binomial(A000041(n/d) + d - 1, d).

Example

The a(4) = 9 partitions of partitions where all partitions have the same sum:
(4), (31), (22), (211), (1111),
(2)(2), (2)(11), (11)(11),
(1)(1)(1)(1).

Mathematica

Table[Sum[Binomial[PartitionsP[n/k]+k-1, k], {k, Divisors[n]}], {n, 60}]

Prog

(PARI) a(n)={if(n<1, n==0, sumdiv(n, d, binomial(numbpart(n/d) + d - 1, d)))} \\ Andrew Howroyd, Jun 22 2018

Crossrefs

Cf. A000005, A001970, A001315, A007716, A038041, A055887, A063834, A271619, A289078, A298422, A306017.

Sequence in context: A317099 A317715 A372121 * A306018 A076120 A082188

Adjacent sequences: A305548 A305549 A305550 * A305552 A305553 A305554

Keyword

nonn

Author

Gus Wiseman, Jun 20 2018

Status

approved