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A308381 Expansion of e.g.f. exp(Sum_{k>=1} x^(k^2)*(2 + x^(k^2))/(2*k^2)). 1
1, 1, 2, 4, 16, 56, 256, 1072, 11264, 119296, 1075456, 9088256, 85292032, 894690304, 8968964096, 90882789376, 2409397682176, 40515889528832, 1051789297844224, 16251803853193216, 302342408330018816, 4444559976664662016, 84010278329827459072, 1289319649553742823424 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

E.g.f.: exp(Sum_{k>=1} A053866(k)*x^k/k).

E.g.f.: Product_{k>=1} 1/(1 - x^(2*k-1))^(lambda(2*k-1)/(2*k-1)), where lambda() is the Liouville function (A008836).

MATHEMATICA

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

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

CROSSREFS

Cf. A008836, A053866, A205801, A306831.

Sequence in context: A053498 A005388 A053503 * A153957 A068789 A009624

Adjacent sequences:  A308378 A308379 A308380 * A308382 A308383 A308384

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 23 2019

STATUS

approved

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Last modified October 18 18:56 EDT 2019. Contains 328197 sequences. (Running on oeis4.)