A318976 Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(phi(k)/k), where phi is the Euler totient function A000010.

1, 2, 6, 32, 196, 1512, 13384, 135872, 1545744, 19441952, 268386784, 4018603008, 65021744704, 1127284876928, 20880206388864, 410781080941568, 8561002328678656, 188224613741879808, 4355496092560324096, 105752112730661347328, 2688539359466319184896

Offset

0,2

Comments

Convolution of A088009 and A000262.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..440

Formula

E.g.f.: exp(x*(2 + x)/(1 - x^2)).

a(n) ~ 2^(-3/4) * 3^(1/4) * exp(sqrt(6*n) - n - 1/2) * n^(n - 1/4).

Mathematica

nmax = 20; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^(EulerPhi[k]/k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
nmax = 20; CoefficientList[Series[E^(x*(2 + x)/(1 - x^2)), {x, 0, nmax}], x] * Range[0, nmax]!

Crossrefs

Cf. A000262, A088009, A318814, A318977.

Cf. A318975, A301555, A301554.

Sequence in context: A271958 A354662 A055596 * A109572 A011820 A206300

Adjacent sequences: A318973 A318974 A318975 * A318977 A318978 A318979

Keyword

nonn

Author

Vaclav Kotesovec, Sep 06 2018

Status

approved