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%I #9 Jun 18 2020 03:24:53
%S 0,1,4,10,23,46,88,158,274,459,748,1190,1858,2846,4292,6384,9373,
%T 13602,19536,27782,39158,54740,75928,104562,143036,194423,262704,
%U 352988,471778,627382,830352,1093994,1435132,1874920,2439832,3163020,4085825,5259602,6748136
%N G.f.: Sum_{k>=1} x^k/(1-x^k) * Product_{k>=1} (1+x^k)/(1-x^k).
%C Convolution of A006128 and A000009.
%C Convolution of A305082 and A000041.
%C Convolution of A000005 and A015128.
%C a(n) is the number of non-overlined parts in all overpartitions of n. - _Joerg Arndt_, Jun 18 2020
%H Vaclav Kotesovec, <a href="/A305102/b305102.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ exp(Pi*sqrt(n)) * (2*gamma + log(4*n/Pi^2)) / (8*Pi*sqrt(n)), where gamma is the Euler-Mascheroni constant A001620.
%t nmax = 40; CoefficientList[Series[Sum[x^k/(1-x^k), {k, 1, nmax}] * Product[(1+x^k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%o (PARI) my(N=44, q='q+O('q^N)); Vec( prod(k=1,N, (1+q^k)/(1-q^k)) * sum(k=1,N, 1*q^k/(1-q^k)) ) \\ _Joerg Arndt_, Jun 18 2020
%Y Cf. A006128, A015723, A209423, A305082, A305101.
%Y Cf. A335651 and A335666.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, May 25 2018
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