A306831 Expansion of e.g.f. exp(Sum_{k>=1} x^(k^2)*(1 + x^(k^2))/k^2).

1, 1, 3, 7, 31, 111, 601, 2773, 27777, 230401, 2484811, 22999791, 254852863, 2615840527, 29661610161, 321837060301, 5736337960321, 86729871740673, 2360637009669907, 39094827261418711, 883743994410948831, 14306422917625170991, 301121907924200191753

Offset: 0

Author

Ilya Gutkovskiy, May 23 2019

Keywords

• nonn

Crossrefs

Cf. A008836, A053866, A205801, A308381.

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)^((-1)^k LiouvilleLambda[k]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

Formula

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