

A279360


Expansion of Product_{k>=1} (1+2*x^(k^2)).


4



1, 2, 0, 0, 2, 4, 0, 0, 0, 2, 4, 0, 0, 4, 8, 0, 2, 4, 0, 0, 4, 8, 0, 0, 0, 6, 12, 0, 0, 12, 24, 0, 0, 0, 4, 8, 2, 4, 8, 16, 4, 12, 8, 0, 0, 12, 24, 0, 0, 10, 28, 16, 4, 12, 24, 32, 8, 16, 4, 8, 0, 12, 32, 16, 2, 32, 56, 0, 4, 16, 24, 16, 0, 4, 36, 56, 0, 16
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OFFSET

0,2


LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000


FORMULA

a(n) ~ c^(1/3) * exp(3 * 2^(4/3) * c^(2/3) * Pi^(1/3) * n^(1/3)) / (3 * 2^(2/3) * Pi^(1/3) * n^(5/6)), where c = PolyLog(3/2, 2) = 1.28138038315976963883198... .  Vaclav Kotesovec, Dec 12 2016


MATHEMATICA

nmax = 200; CoefficientList[Series[Product[(1+2*x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 200; nn = Floor[Sqrt[nmax]]+1; poly = ConstantArray[0, nn^2 + 1]; poly[[1]] = 1; poly[[2]] = 2; poly[[3]] = 0; Do[Do[poly[[j + 1]] += 2*poly[[j  k^2 + 1]], {j, nn^2, k^2, 1}]; , {k, 2, nn}]; Take[poly, nmax+1]


CROSSREFS

Cf. A032302, A033461, A279226, A279368.
Sequence in context: A250023 A151669 A115509 * A134312 A329790 A195581
Adjacent sequences: A279357 A279358 A279359 * A279361 A279362 A279363


KEYWORD

nonn


AUTHOR

Vaclav Kotesovec, Dec 10 2016


STATUS

approved



