A092314 Sum of smallest parts of all partitions of n into odd parts.

1, 1, 4, 2, 7, 6, 11, 8, 18, 16, 24, 23, 34, 36, 51, 48, 66, 74, 90, 98, 126, 137, 164, 182, 220, 247, 294, 324, 380, 434, 496, 556, 650, 728, 835, 938, 1068, 1204, 1372, 1531, 1736, 1956, 2198, 2462, 2784, 3104, 3482, 3890, 4358, 4864, 5441, 6048, 6748, 7516

Offset

1,3

Comments

a(n) = Sum_{k>=1} k*A116856(n,k). - Emeric Deutsch, Feb 24 2006

Links

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

Formula

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

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

Example

a(5)=7 because the partitions of 5 into odd parts are [5],[3,1,1] and [1,1,1,1,1] and the smallest parts add up to 5+1+1=7.

Maple

g:=sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1), k=n..30), n=1..30): gser:=series(g, x=0, 57): seq(coeff(gser, x^n), n=1..54); # Emeric Deutsch, Feb 24 2006

Mathematica

nmax = 50; Rest[CoefficientList[Series[Sum[(2*n - 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. A092322, A092269, A092309, A092321, A092313, A092310, A092311, A092268.

Cf. A116856, A092322.

Sequence in context: A016695 A125271 A245262 * A237750 A372860 A249652

Adjacent sequences: A092311 A092312 A092313 * A092315 A092316 A092317

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 15 2004

Extensions

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

Status

approved