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%I #22 Mar 10 2019 19:34:53
%S 0,1,2,4,6,9,14,19,26,36,48,62,82,104,132,169,210,260,324,396,484,592,
%T 714,860,1036,1238,1474,1756,2078,2452,2894,3396,3976,4654,5422,6309,
%U 7332,8490,9816,11338,13060,15018,17254,19774,22630,25878,29524,33642
%N Total number of parts in all partitions of n into odd parts.
%C Starting with "1" = triangle A097304 * [1, 2, 3, ...]. - _Gary W. Adamson_, Apr 09 2010
%H Vaclav Kotesovec, <a href="/A067588/b067588.txt">Table of n, a(n) for n = 0..10000</a>
%H Cristina Ballantine, Mircea Merca, <a href="https://doi.org/10.1016/j.jnt.2016.06.007">New convolutions for the number of divisors</a>, Journal of Number Theory, 2016, vol. 170, pp. 17-34.
%F 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
%F G.f.: Sum_{n>0} n*x^n/Product_{k=1..n} (1-x^(2*k)). - _Vladeta Jovovic_, Dec 15 2003
%F 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
%Y Cf. A067589, A006128, A066897, A066898.
%Y Cf. A097304. - _Gary W. Adamson_, Apr 09 2010
%K easy,nonn
%O 0,3
%A _Naohiro Nomoto_, Jan 31 2002
%E Corrected by _James A. Sellers_, May 31 2007
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