A305123 G.f.: Sum_{k>=1} x^(2*k-1)/(1+x^(2*k-1)) * Product_{k>=1} 1/(1-x^k).

0, 1, 0, 3, 2, 7, 6, 15, 16, 32, 36, 62, 74, 117, 142, 214, 264, 377, 468, 648, 806, 1090, 1354, 1791, 2224, 2894, 3580, 4598, 5670, 7193, 8838, 11102, 13588, 16925, 20632, 25501, 30972, 38021, 46000, 56135, 67668, 82119, 98642, 119115, 142592, 171412, 204520

Offset: 0

Author

Vaclav Kotesovec, May 26 2018

Keywords

• nonn

Comments

Conjecture: a(n) is odd iff n is a term of A067567. - Peter Bala, Jan 10 2025

Links

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

Crossrefs

Cf. A000041, A001227, A006128, A067567, A209423, A066898, A305121, A066897.

Cf. A116676, A305124.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Sum[x^(2*k-1)/(1+x^(2*k-1)), {k, 1, nmax}] * Product[1/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

For n > 0, a(n) = A209423(n) - A305121(n).

a(n) ~ log(2) * exp(Pi*sqrt(2*n/3)) / (2^(5/2)*Pi*sqrt(n)).