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

Author

Gus Wiseman, Jun 20 2018

Keywords

• nonn

Examples

			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).
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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