A092268 Total number of smallest parts in all partitions of n into odd parts.

1, 2, 4, 5, 8, 12, 15, 20, 29, 36, 46, 61, 74, 95, 122, 145, 180, 224, 268, 328, 399, 474, 567, 682, 807, 955, 1136, 1330, 1564, 1842, 2140, 2499, 2914, 3375, 3917, 4533, 5220, 6014, 6929, 7942, 9102, 10430, 11898, 13582, 15489, 17600, 19999, 22706, 25719

Offset

1,2

Links

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

Formula

G.f.: Sum((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+3+2+1=12.

Mathematica

nmax = 50; Rest[CoefficientList[Series[Sum[(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, A092313, A092310, A092311.

Cf. A067588.

Sequence in context: A344841 A035001 A260386 * A335702 A069259 A102186

Adjacent sequences: A092265 A092266 A092267 * A092269 A092270 A092271

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 16 2004

Extensions

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

Status

approved