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

Author

Vladeta Jovovic, Feb 15 2004

Keywords

• easy
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A092322, A092269, A092309, A092321, A092313, A092310, A092311, A092268.

Cf. A116856, A092322.

Programs

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 *)

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

Extensions

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