A092322 Sum of largest parts of all partitions of n into odd parts.

1, 1, 4, 4, 9, 12, 19, 24, 36, 48, 64, 83, 108, 140, 179, 224, 280, 352, 432, 532, 652, 795, 960, 1160, 1392, 1669, 1992, 2368, 2804, 3320, 3908, 4592, 5388, 6300, 7349, 8560, 9940, 11524, 13340, 15401, 17752, 20436, 23472, 26920, 30840, 35256, 40252, 45900

Offset

1,3

Comments

a(n) = Sum_{k>=1} k*A116799(n,k). - Emeric Deutsch, Feb 24 2006

Links

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

Formula

G.f.: Sum_{n>=1} (2*n-1)*x^(2*n-1)/Product_{k=1..n} (1-x^(2*k-1)).

Example

a(5)=9 because the partitions of 5 into odd parts are [5],[3,1,1] and [1,1,1,1,1] and the largest parts add up to 5+3+1=9.

Maple

g:=sum((2*n-1)*x^(2*n-1)/Product(1-x^(2*k-1), k=1..n), n=1..30): gser:=series(g, x=0, 50): seq(coeff(gser, x^n), n=1..48); # 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, 1, n}], {n, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 06 2019 *)

Crossrefs

Cf. A092314, A092269, A092309, A092321, A092313, A092310, A092311, A092268.

Cf. A116799.

Sequence in context: A168157 A222045 A088190 * A341678 A050218 A165996

Adjacent sequences: A092319 A092320 A092321 * A092323 A092324 A092325

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 15 2004

Extensions

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

Status

approved