A321508 Expansion of Product_{k>=1} 1/(1 - x^prime(k))^A056768(k).

1, 0, 1, 1, 1, 3, 2, 6, 4, 7, 10, 15, 17, 30, 31, 41, 58, 81, 105, 143, 177, 218, 306, 393, 550, 618, 883, 1024, 1395, 1810, 2372, 2985, 3682, 4762, 6077, 7634, 10160, 12517, 15448, 19820, 24754, 32108, 40085, 50851, 62331, 78548, 98505, 125596, 156565

Offset

0,6

Comments

a(n) is the number of partitions of n into prime parts prime(k) of A056768(k) kinds.

Links

Table of n, a(n) for n=0..48.

Index entries for sequences related to partitions

Formula

G.f.: Product_{k>=1} 1/(1 - x^A000040(k))^A000607(A000040(k)).

Example

a(7) = 6 because we have [{7}], [{5, 2}], [{5}, {2}], [{3, 2, 2}], [{3, 2}, {2}] and [{3}, {2}, {2}].

Mathematica

b[n_] := b[n] = SeriesCoefficient[Product[1/(1 - x^Prime[k]), {k, 1, n}], {x, 0, Prime[n]}]; a[n_] := a[n] = SeriesCoefficient[Product[1/(1 - x^Prime[k])^b[k], {k, 1, n}], {x, 0, n}]; Table[a[n], {n, 0, 48}]

Crossrefs

Cf. A000040, A000607, A001970, A056768, A300300.

Sequence in context: A267104 A093050 A289194 * A245261 A054089 A365312

Adjacent sequences: A321505 A321506 A321507 * A321509 A321510 A321511

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 11 2018

Status

approved