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A067588 Total number of parts in all partitions of n into odd parts. 9
0, 1, 2, 4, 6, 9, 14, 19, 26, 36, 48, 62, 82, 104, 132, 169, 210, 260, 324, 396, 484, 592, 714, 860, 1036, 1238, 1474, 1756, 2078, 2452, 2894, 3396, 3976, 4654, 5422, 6309, 7332, 8490, 9816, 11338, 13060, 15018, 17254, 19774, 22630, 25878, 29524, 33642 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Starting with "1" = triangle A097304 * [1, 2, 3, ...]. - Gary W. Adamson, Apr 09 2010

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Cristina Ballantine, Mircea Merca, New convolutions for the number of divisors, Journal of Number Theory, 2016, vol. 170, pp. 17-34.

FORMULA

G.f.: G(x)*H(x) where G(x) = Sum_{k>=1) x^(2*k-1)/(1-x^(2*k-1)) is g.f. for the number of odd divisors of n (cf. A001227) and H(x) = Product_{k>=1) (1+x^k) is g.f. for the number of partitions of n into odd parts (cf. A000009). Convolution of A001227 and A000009: Sum_{k=0..n} A001227(k)*A000009(n-k). - Vladeta Jovovic, Feb 04 2002

G.f.: Sum_{n>0} n*x^n/Product_{k=1..n} (1-x^(2*k)). - Vladeta Jovovic, Dec 15 2003

a(n) ~ 3^(1/4) * (2*gamma + log(48*n/Pi^2)) * exp(Pi*sqrt(n/3)) / (8*Pi*n^(1/4)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, May 25 2018

CROSSREFS

Cf. A067589, A006128, A066897, A066898.

Cf. A097304. - Gary W. Adamson, Apr 09 2010

Sequence in context: A113753 A024457 A117842 * A003402 A218004 A034748

Adjacent sequences:  A067585 A067586 A067587 * A067589 A067590 A067591

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto, Jan 31 2002

EXTENSIONS

Corrected by James A. Sellers, May 31 2007

STATUS

approved

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Last modified October 15 05:43 EDT 2019. Contains 328026 sequences. (Running on oeis4.)