A305122 G.f.: Sum_{k>=1} x^(2*k)/(1+x^(2*k)) * Product_{k>=1} (1+x^k)/(1-x^k).

0, 0, 1, 2, 4, 8, 16, 28, 47, 78, 126, 198, 306, 464, 694, 1024, 1490, 2146, 3061, 4322, 6052, 8408, 11592, 15872, 21592, 29192, 39242, 52468, 69788, 92376, 121716, 159664, 208569, 271372, 351732, 454228, 584546, 749720, 958472, 1221560, 1552210, 1966698

Offset

0,4

Comments

Convolution of A305121 and A000009.

Links

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

Formula

a(n) = A305101(n) - A305124(n).

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

Mathematica

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

Crossrefs

Cf. A305102, A305101, A305104, A305105, A305124.

Cf. A116680, A305121.

Sequence in context: A057975 A260881 A089055 * A276677 A112128 A208933

Adjacent sequences: A305119 A305120 A305121 * A305123 A305124 A305125

Keyword

nonn

Author

Vaclav Kotesovec, May 26 2018

Status

approved