A305124 G.f.: Sum_{k>=1} x^(2*k-1)/(1+x^(2*k-1)) * Product_{k>=1} (1+x^k)/(1-x^k).

0, 1, 1, 4, 7, 14, 24, 42, 69, 113, 178, 276, 420, 630, 930, 1360, 1963, 2804, 3969, 5568, 7746, 10700, 14672, 19986, 27060, 36423, 48754, 64928, 86038, 113478, 149012, 194842, 253737, 329172, 425452, 547952, 703343, 899858, 1147680, 1459364, 1850310, 2339432

Offset: 0

Author

Vaclav Kotesovec, May 26 2018

Keywords

• nonn

Comments

Convolution of A305123 and A000009.

Links

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

Crossrefs

Cf. A305102, A305101, A305104, A305122, A305105.

Cf. A116676, A305123.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Sum[x^(2*k-1)/(1+x^(2*k-1)), {k, 1, nmax}] * Product[(1+x^k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) = A305101(n) - A305122(n).

a(n) ~ exp(sqrt(n)*Pi) * log(2) / (8*Pi*sqrt(n)).