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 A308397 Expansion of e.g.f. exp(Sum_{k>=1} x^(k^2)*(1 - x^(k^2))/k^2). 3

%I

%S 1,1,-1,-5,7,71,-59,-1511,-9295,-1583,861751,4039091,-80670281,

%T -606807785,7674244397,78614840641,1146707474401,12874145737889,

%U -1054507266321425,-19048413877999253,238097060642380391,6646823785301856871,-59731575523361439851,-2231444370433747995415

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

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

%t 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]!

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

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

%K sign

%O 0,4

%A _Ilya Gutkovskiy_, May 24 2019

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Last modified June 16 02:14 EDT 2021. Contains 345055 sequences. (Running on oeis4.)