A308398 Expansion of e.g.f. exp(Sum_{k>=1} x^(k^2)*(x^(k^2) - 1)/k^2).

1, -1, 3, -7, 19, -51, 61, 167, 6777, -107929, 1650691, -17839911, 157217083, -1229269627, 6185945949, -3251776921, -1151787785999, 10138302541647, 532690324952707, -14122245788830279, 443912721023736291, -7480012715591067331, 115775303074594208893, -1392396864130912381017

Offset: 0

Author

Ilya Gutkovskiy, May 24 2019

Keywords

• sign

Crossrefs

Cf. A008836, A118208, A190585, A205801, A306831, A308396, A308397.

Programs

Mathematica

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

Formula

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