A318975 Expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^phi(k), where phi is the Euler totient function A000010.

1, 2, 4, 10, 20, 42, 80, 154, 288, 522, 940, 1658, 2892, 4970, 8456, 14218, 23696, 39122, 64044, 104042, 167732, 268602, 427248, 675482, 1061632, 1659298, 2579676, 3990418, 6142892, 9412906, 14360136, 21814698, 33004704, 49739426, 74677924, 111713658

Offset

0,2

Comments

Convolution of A299069 and A061255.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Example

a(n) ~ exp(3^(4/3) * (7*Zeta(3))^(1/3) * n^(2/3) / (2*Pi^(2/3)) - 1/6) * A^2 * (7*Zeta(3))^(1/9) / (sqrt(2) * 3^(7/18) * Pi^(8/9) * n^(11/18)), where A is the Glaisher-Kinkelin constant A074962.

Mathematica

nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^EulerPhi[k], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A061255, A299069, A301554, A301555.

Cf. A318976, A318814, A318977.

Sequence in context: A236572 A283213 A283251 * A255386 A167030 A026644

Adjacent sequences: A318972 A318973 A318974 * A318976 A318977 A318978

Keyword

nonn

Author

Vaclav Kotesovec, Sep 06 2018

Status

approved