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

1,2

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 = 1 .. n), n = 1 .. infinity).

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

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 *)

Crossrefs

Cf. A092314, A092322, A092269, A092309, A092321, A092313, A092311, A092268.

Sequence in context: A334906 A078471 A127406 * A306924 A087376 A199974

Adjacent sequences: A092307 A092308 A092309 * A092311 A092312 A092313

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 16 2004

Extensions

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

Status

approved