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A305101
G.f.: Sum_{k>=1} x^k/(1+x^k) * Product_{k>=1} (1+x^k)/(1-x^k).
4
0, 1, 2, 6, 11, 22, 40, 70, 116, 191, 304, 474, 726, 1094, 1624, 2384, 3453, 4950, 7030, 9890, 13798, 19108, 26264, 35858, 48652, 65615, 87996, 117396, 155826, 205854, 270728, 354506, 462306, 600544, 777184, 1002180, 1287889, 1649578, 2106152, 2680924
OFFSET
0,3
COMMENTS
Convolution of A209423 and A000009.
Convolution of A015723 and A000041.
Convolution of A048272 and A015128.
a(n) is the number of overlined parts in all overpartitions of n. - Joerg Arndt, Jun 18 2020
FORMULA
a(n) ~ exp(sqrt(n)*Pi) * log(2) / (4*Pi*sqrt(n)).
a(n) = A305122(n) + A305124(n).
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]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 25 2018
STATUS
approved