A308397 Expansion of e.g.f. exp(Sum_{k>=1} x^(k^2)*(1 - x^(k^2))/k^2).

1, 1, -1, -5, 7, 71, -59, -1511, -9295, -1583, 861751, 4039091, -80670281, -606807785, 7674244397, 78614840641, 1146707474401, 12874145737889, -1054507266321425, -19048413877999253, 238097060642380391, 6646823785301856871, -59731575523361439851, -2231444370433747995415

Offset: 0

Author

Ilya Gutkovskiy, May 24 2019

Keywords

• sign

Crossrefs

Cf. A008836, A118207, A190585, A205801, A306831, A308396, A308398.

Programs

Mathematica

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

Formula

E.g.f.: Product_{k>=1} (1 + x^k)^(lambda(k)/k), where lambda() is the Liouville function (A008836).