A308392 Expansion of e.g.f. exp(x + 2 * Sum_{k>=1} x^(2^k)/2^k).

1, 1, 3, 7, 37, 141, 871, 4243, 42057, 285337, 3008971, 23292831, 295839853, 2733811237, 35818366767, 360892885291, 8394097115281, 113063153955633, 2347668770502547, 32362689647446327, 744513384520939701, 11439249110436735421, 245772094687992577783, 3860080495614830875587

Offset: 0

Author

Ilya Gutkovskiy, May 24 2019

Keywords

• nonn

Crossrefs

Cf. A005388, A008683.

Programs

Mathematica

nmax = 23; CoefficientList[Series[Exp[x + 2 Sum[x^(2^k)/2^k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Product[(1 - x^k)^((-1)^k MoebiusMu[k]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: Product_{k>=1} (1 - x^k)^((-1)^k*mu(k)/k).

E.g.f.: exp(-x)*g(x)^2, where g(x) = e.g.f. of A005388.