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A092311 Total number of largest parts in all partitions of n into odd parts. 16
1, 2, 4, 5, 7, 10, 12, 14, 19, 23, 26, 33, 38, 44, 56, 63, 71, 88, 99, 114, 138, 155, 176, 208, 237, 269, 314, 357, 402, 468, 529, 594, 686, 772, 873, 999, 1119, 1260, 1431, 1608, 1804, 2039, 2284, 2554, 2884, 3219, 3590, 4032, 4493, 5011, 5603, 6231, 6928 (list; graph; refs; listen; history; text; internal format)
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=1..n), n=1..infinity).

a(n) ~ exp(Pi*sqrt(n/3)) / (4 * 3^(1/4) * n^(3/4)). - 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+1+2+1=10.

MATHEMATICA

nmax = 50; Rest[CoefficientList[Series[Sum[(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, A092310, A092268.

Sequence in context: A325124 A231013 A231008 * A186386 A247589 A058212

Adjacent sequences:  A092308 A092309 A092310 * A092312 A092313 A092314

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 16 2004

EXTENSIONS

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

STATUS

approved

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Last modified July 21 07:23 EDT 2019. Contains 325192 sequences. (Running on oeis4.)