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

Author

Vaclav Kotesovec, Sep 06 2018

Keywords

• nonn

Comments

Convolution of A088009 and A000262.

Links

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

Crossrefs

Cf. A000262, A088009, A318814, A318977.

Cf. A318975, A301555, A301554.

Programs

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]!

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).