login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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 A195581 A020474

Adjacent sequences:  A279357 A279358 A279359 * A279361 A279362 A279363

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Dec 10 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 22 05:58 EST 2018. Contains 299430 sequences. (Running on oeis4.)