A298436 Expansion of Product_{k>=1} 1/(1 - x^prime(k))^2.

1, 0, 2, 2, 3, 6, 7, 12, 15, 22, 30, 40, 54, 72, 93, 122, 157, 202, 256, 326, 409, 512, 640, 792, 981, 1204, 1479, 1802, 2196, 2662, 3218, 3880, 4660, 5588, 6677, 7960, 9471, 11232, 13299, 15710, 18514, 21784, 25570, 29968, 35047, 40922, 47698, 55500, 64480, 74786, 86618

Offset: 0

Author

Ilya Gutkovskiy, Jan 19 2018

Keywords

• nonn

Comments

Number of partitions of n into prime parts of 2 kinds.

Self-convolution of A000607.

Examples

			a(5) = 6 because we have [5a], [5b], [3a, 2a], [3a, 2b], [3b, 2a] and [3b, 2b].
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Seiichi Manyama)
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000040, A000607, A000712, A280245.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[1/(1 - x^Prime[k])^2, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} 1/(1 - x^prime(k))^2.

log(a(n)) ~ 2*Pi*sqrt(2*n/(3*log(n/2))). - Vaclav Kotesovec, Jan 12 2021