A280663 G.f.: Product_{k>=1, j>=1} (1 + x^(j*k^3)).

1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 11, 14, 17, 21, 26, 32, 39, 47, 57, 68, 81, 97, 115, 136, 162, 190, 223, 263, 306, 357, 417, 483, 561, 650, 750, 866, 997, 1145, 1315, 1507, 1725, 1971, 2250, 2564, 2917, 3318, 3766, 4270, 4840, 5475, 6188, 6990, 7881, 8881

Offset

0,4

Links

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

Formula

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

Mathematica

nmax = 100; CoefficientList[Series[Product[1+x^(j*k^3), {k, 1, Floor[nmax^(1/3)]+1}, {j, 1, Floor[nmax/k^3]+1}], {x, 0, nmax}], x]

Crossrefs

Cf. A107742, A280451, A280664.

Sequence in context: A326491 A266748 A304883 * A052816 A122130 A003073

Adjacent sequences: A280660 A280661 A280662 * A280664 A280665 A280666

Keyword

nonn

Author

Vaclav Kotesovec, Jan 07 2017

Status

approved