A092310 Sum of largest parts (counted with multiplicity) of all partitions of n into odd parts.

1, 2, 6, 7, 13, 20, 28, 34, 53, 71, 88, 117, 148, 188, 250, 301, 365, 472, 565, 688, 860, 1027, 1224, 1486, 1771, 2107, 2524, 2983, 3496, 4158, 4867, 5666, 6676, 7762, 9021, 10525, 12145, 14034, 16249, 18696, 21478, 24721, 28308, 32364, 37110, 42289

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+1*3+2*3+1*5=20.
		

Links

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

Crossrefs

Cf. A092314, A092322, A092269, A092309, A092321, A092313, 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, 1, n}], {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 = 1 .. n), n = 1 .. infinity).

Extensions

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