A280254 Expansion of 1/(1 - Sum_{k>=1} x^p(k)), where p(k) is the number of partitions of k (A000041).

1, 1, 2, 4, 7, 14, 26, 50, 95, 180, 343, 652, 1240, 2358, 4484, 8528, 16217, 30840, 58649, 111532, 212101, 403352, 767056, 1458711, 2774031, 5275379, 10032192, 19078230, 36281088, 68995780, 131209344, 249520934, 474514204, 902384123, 1716064761, 3263442024, 6206090863, 11802129022, 22444120219

Offset: 0

Author

Ilya Gutkovskiy, Dec 30 2016

Keywords

• nonn

Comments

Number of compositions (ordered partitions) into partition numbers.

Examples

			a(4) = 7 because we have [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2] and [1, 1, 1, 1].
		

Links

• Eric Weisstein's World of Mathematics, Partition Function P
• Index entries for sequences related to compositions

Crossrefs

Cf. A000041, A007279.

Programs

Mathematica

nmax = 38; CoefficientList[Series[1/(1 - Sum[x^PartitionsP[k], {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^p(k)).