A293466 a(n) = Sum_{k=0..n} 2^k * q(k), where q(k) is A000009 (partitions into distinct parts).

1, 3, 7, 23, 55, 151, 407, 1047, 2583, 6679, 16919, 41495, 102935, 250391, 610839, 1495575, 3592727, 8573463, 20632087, 48943639, 116052503, 275436055, 648729111, 1521144343, 3567964695, 8332694039, 19405656599, 45175460375, 104768131607, 242207085079

Offset: 0

Author

Vaclav Kotesovec, Oct 09 2017

Keywords

• nonn

Crossrefs

Cf. A025147, A259400, A293465.

Programs

Mathematica

Table[Sum[2^k * PartitionsQ[k], {k, 0, n}], {n, 0, 30}]

Formula

a(n) ~ 2^(n-1) * exp(Pi*sqrt(n/3)) / (3^(1/4) * n^(3/4)).