A092313 Sum of smallest parts (counted with multiplicity) of all partitions of n into odd parts.

1, 2, 6, 5, 12, 16, 21, 22, 43, 46, 60, 75, 92, 119, 164, 167, 220, 276, 320, 390, 491, 562, 665, 796, 949, 1109, 1342, 1530, 1804, 2144, 2442, 2843, 3342, 3837, 4471, 5147, 5894, 6780, 7841, 8910, 10204, 11718, 13282, 15168, 17337, 19594, 22225, 25210

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..2500

Formula

G.f.: Sum((2*n-1)*x^(2*n-1)/(1-x^(2*n-1))/Product(1-x^(2*k-1), k = n .. infinity), n = 1 .. infinity).

a(n) ~ 3^(1/4) * exp(Pi*sqrt(n/3)) / (2*Pi*n^(1/4)). - Vaclav Kotesovec, Jul 07 2019

Example

Partitions of 6 into odd parts are: [1,1,1,1,1,1], [1,1,1,3], [3,3], [1,5]; thus a(6)=6*1+3*1+2*3+1*1=16.

Mathematica

nmax = 50; Rest[CoefficientList[Series[Sum[(2*n - 1)*x^(2*n - 1)/(1 - x^(2*n - 1)) / Product[(1 - x^(2*k - 1)), {k, n, nmax}], {n, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 06 2019 *)

Crossrefs

Cf. A092314, A092322, A092269, A092309, A092321, A092310, A092311, A092268.

Sequence in context: A359035 A179627 A193977 * A318358 A230383 A009460

Adjacent sequences: A092310 A092311 A092312 * A092314 A092315 A092316

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 16 2004

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004

Status

approved