A308461 Expansion of e.g.f. exp(x + 2 * Sum_{k>=2} x^(2^k)/2^k).

1, 1, 1, 1, 13, 61, 181, 421, 15961, 137593, 682921, 2498761, 77344741, 927575221, 6402167773, 31881065581, 4104839160241, 68050288734961, 609856397747281, 3857727706737553, 222655237411428541, 4351842324095032621, 47276537013742616581, 361153046139022585141

Offset: 0

Author

Ilya Gutkovskiy, May 28 2019

Keywords

• nonn

Crossrefs

Cf. A000321, A005388, A008683, A308392.

Programs

Mathematica

nmax = 23; CoefficientList[Series[Exp[x + 2 Sum[x^(2^k)/2^k, {k, 2, 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*(1 + x))*g(x)^2, where g(x) = e.g.f. of A005388.