A301971 a(n) = [x^n] Product_{k>=1} 1/(1 - x^prime(k))^n.

1, 0, 2, 3, 10, 30, 77, 252, 682, 2136, 6182, 18766, 56173, 169351, 512990, 1551828, 4720170, 14348289, 43751984, 133502873, 408029510, 1248460587, 3823949824, 11724787763, 35980251181, 110510334780, 339674840715, 1044812449722, 3215861978150, 9904301974294, 30521063942312, 94103983534015

Offset: 0

Author

Ilya Gutkovskiy, Mar 29 2018

Keywords

• nonn

Comments

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

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A000607, A008485, A030009, A117278, A219224, A259254, A291647, A298436, A299168.

Programs

Mathematica

Table[SeriesCoefficient[Product[1/(1 - x^Prime[k])^n, {k, 1, n}], {x, 0, n}], {n, 0, 31}]