A308396 Expansion of e.g.f. exp(-Sum_{k>=1} x^(k^2)/k^2).

1, -1, 1, -1, -5, 29, -89, 209, 841, -50905, 458641, -2423521, 8243731, 158742869, -2450634185, 18519809489, -1402926535919, 21355930009679, -139305034406879, 306503668195775, 40578438892908331, -816475138658703091, 6941097158619626311, -24787202385366731311

Offset: 0

Author

Ilya Gutkovskiy, May 24 2019

Keywords

• sign

Crossrefs

Cf. A008836, A118205, A190585, A205801, A306831, A308397, A308398.

Programs

Mathematica

nmax = 23; CoefficientList[Series[Exp[-Sum[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).