A305102 G.f.: Sum_{k>=1} x^k/(1-x^k) * Product_{k>=1} (1+x^k)/(1-x^k).

0, 1, 4, 10, 23, 46, 88, 158, 274, 459, 748, 1190, 1858, 2846, 4292, 6384, 9373, 13602, 19536, 27782, 39158, 54740, 75928, 104562, 143036, 194423, 262704, 352988, 471778, 627382, 830352, 1093994, 1435132, 1874920, 2439832, 3163020, 4085825, 5259602, 6748136

Offset: 0

Author

Vaclav Kotesovec, May 25 2018

Keywords

• nonn

Comments

Convolution of A006128 and A000009.

Convolution of A305082 and A000041.

Convolution of A000005 and A015128.

a(n) is the number of non-overlined parts in all overpartitions of n. - Joerg Arndt, Jun 18 2020

Links

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

Crossrefs

Cf. A006128, A015723, A209423, A305082, A305101.

Cf. A335651 and A335666.

Programs

Mathematica

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]

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

Formula

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.