A301589 Expansion of Product_{k>=1} 1/(1 - x^k)^(mod(k,3)).

1, 1, 3, 3, 7, 9, 15, 20, 31, 41, 61, 79, 113, 146, 201, 260, 349, 447, 589, 748, 972, 1226, 1571, 1968, 2495, 3106, 3900, 4825, 6008, 7392, 9137, 11181, 13731, 16719, 20409, 24737, 30032, 36243, 43783, 52620, 63282, 75760, 90727, 108222, 129097, 153464

Offset

0,3

Comments

Euler transform of A010872.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^(2/3) / (2^(5/6) * 3^(7/6) * Gamma(1/3) * n^(5/6)).

Mathematica

nmax = 60; CoefficientList[Series[Product[1/(1-x^k)^Mod[k, 3], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A010872, A301588.

Sequence in context: A131036 A331788 A206433 * A237666 A285187 A034411

Adjacent sequences: A301586 A301587 A301588 * A301590 A301591 A301592

Keyword

nonn

Author

Vaclav Kotesovec, Mar 24 2018

Status

approved