A280277 G.f.: Product_{k>=1} (1 + x^k) / (1 - x^(k^3)).

1, 2, 3, 5, 7, 10, 14, 19, 26, 35, 46, 60, 77, 98, 124, 156, 195, 242, 299, 367, 448, 545, 660, 796, 957, 1146, 1368, 1629, 1933, 2287, 2700, 3178, 3732, 4373, 5112, 5964, 6944, 8068, 9357, 10832, 12517, 14440, 16632, 19126, 21960, 25178, 28825, 32954, 37625

Offset

0,2

Comments

Convolution of A000009 and A003108.

Links

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

Vaclav Kotesovec, Graph - The asymptotic ratio (100000 terms)

Formula

a(n) ~ exp(Pi*sqrt(n/3) + 2^(1/3) * Gamma(1/3) * Zeta(4/3) * n^(1/6) / (3^(5/6) * Pi^(1/3))) / (16*sqrt(3)*Pi*n).

Mathematica

nmax=80; CoefficientList[Series[Product[(1+x^k)/(1-x^(k^3)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000009, A003108, A102108, A280264, A280276.

Sequence in context: A023026 A096778 A325862 * A102108 A105780 A001522

Adjacent sequences: A280274 A280275 A280276 * A280278 A280279 A280280

Keyword

nonn

Author

Vaclav Kotesovec, Dec 30 2016

Status

approved