A270105 a(n) = Sum_{k=0..n} k*A000009(k).

0, 1, 3, 9, 17, 32, 56, 91, 139, 211, 311, 443, 623, 857, 1165, 1570, 2082, 2728, 3556, 4582, 5862, 7458, 9416, 11808, 14736, 18286, 22576, 27760, 33976, 41400, 50280, 60820, 73300, 88084, 105492, 125967, 150015, 178135, 210967, 249265, 293785, 345445, 405337

Offset: 0

Author

Vaclav Kotesovec, Mar 12 2016

Keywords

• nonn

Crossrefs

Cf. A000009, A000070, A014153, A036469, A095944, A182738.

Partial sums of A066189.

Programs

Mathematica

Table[Sum[PartitionsQ[k]*k, {k, 0, n}], {n, 0, 50}]

Formula

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

G.f.: x*f'(x)/(1 - x), where f(x) = Product_{k>=1} (1 + x^k). - Ilya Gutkovskiy, Apr 13 2017