A280204 G.f.: Product_{k>=1} (1+x^(k^2)) / (1-x^k).

1, 2, 3, 5, 9, 14, 21, 31, 45, 65, 92, 127, 175, 239, 322, 430, 572, 753, 985, 1281, 1657, 2131, 2727, 3471, 4401, 5558, 6988, 8751, 10924, 13588, 16846, 20819, 25653, 31518, 38621, 47195, 57530, 69958, 84869, 102723, 124070, 149532, 179852, 215894, 258668

Offset

0,2

Comments

Convolution of A033461 and A000041.

Links

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

Formula

a(n) ~ exp(Pi*sqrt(2*n/3) + 2^(-5/4)*3^(1/4)*(sqrt(2)-1)*Zeta(3/2)*n^(1/4) - 3*(sqrt(2)-1)^2*Zeta(3/2)^2/(64*Pi)) / (2^(5/2)*sqrt(3)*n).

Mathematica

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

Crossrefs

Cf. A000041, A033461, A052335, A078434, A087153, A117144, A264393, A280224, A280225, A369520, A369570.

Sequence in context: A023672 A023567 A076027 * A240841 A056686 A326332

Adjacent sequences: A280201 A280202 A280203 * A280205 A280206 A280207

Keyword

nonn

Author

Vaclav Kotesovec, Dec 28 2016

Status

approved