A280917 Expansion of 1/(1 - x - Sum_{k>=1} x^prime(k)).

1, 1, 2, 4, 7, 14, 26, 50, 95, 180, 343, 652, 1240, 2359, 4486, 8532, 16227, 30862, 58697, 111636, 212321, 403814, 768015, 1460691, 2778094, 5283667, 10049027, 19112282, 36349721, 69133673, 131485594, 250072951, 475614693, 904573387, 1720411555, 3272057256, 6223138101, 11835809946, 22510571803, 42812941849

Offset: 0

Author

Ilya Gutkovskiy, Jan 10 2017

Keywords

• nonn

Comments

Number of compositions (ordered partitions) of n into prime parts (1 included) (A008578).

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

• Indranil Ghosh, Table of n, a(n) for n = 0..99
• Index entries for sequences related to compositions

Crossrefs

Cf. A000607, A002124, A008578, A023360, A034891, A036497.

Programs

Mathematica

nmax = 39; CoefficientList[Series[1/(1 - x - Sum[x^Prime[k], {k, 1, nmax}]), {x, 0, nmax}], x]

PARI

Vec(1 / (1 - x - sum(k=1, 100,  x^prime(k))) + O(x^100)) \\ Indranil Ghosh, Mar 09 2017

Formula

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