A291647 Expansion of Product_{k>=1} (1 + x^prime(k))^prime(k).

1, 0, 2, 3, 1, 11, 3, 20, 21, 20, 64, 35, 112, 117, 160, 269, 284, 477, 598, 819, 1116, 1495, 1899, 2718, 3389, 4596, 6121, 7627, 10460, 13128, 17350, 22506, 28696, 37063, 47779, 60249, 78642, 98783, 126058, 160758, 200795, 257750, 321768, 407930, 511526, 640636, 802816, 1005618, 1252820, 1567454, 1946162

Offset: 0

Author

Ilya Gutkovskiy, Aug 28 2017

Keywords

• nonn

Comments

Number of partitions of n into distinct prime parts, where prime(k) different parts of size prime(k) are available (2a, 2b, 3a, 3b, 3c, ...).

Examples

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

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A000040, A000586, A007441, A026007, A061151, A061152, A219224, A262736.

Programs

Mathematica

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

Formula

G.f.: Product_{k>=1} (1 + x^A000040(k))^A000040(k).