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

Author

Vladeta Jovovic, Feb 16 2004

Keywords

• easy
• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

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

Extensions

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