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A308396 Expansion of e.g.f. exp(-Sum_{k>=1} x^(k^2)/k^2). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..23.

FORMULA

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

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]!

CROSSREFS

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

Sequence in context: A050409 A111937 A215850 * A190585 A197276 A211062

Adjacent sequences:  A308393 A308394 A308395 * A308397 A308398 A308399

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, May 24 2019

STATUS

approved

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Last modified June 13 04:53 EDT 2021. Contains 344980 sequences. (Running on oeis4.)