The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A285288 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A285288

Expansion of Product_{k>=0} (1 + x^(4*k+1))^(4*k+1).
(history; published version)

#14 by Joerg Arndt at Sun Apr 16 10:27:29 EDT 2017

STATUS

proposed

approved

#13 by Seiichi Manyama at Sun Apr 16 10:21:04 EDT 2017

STATUS

editing

proposed

#12 by Seiichi Manyama at Sun Apr 16 10:20:58 EDT 2017

LINKS

Seiichi Manyama, <a href="/A285288/b285288.txt">Table of n, a(n) for n = 0..10000</a>

STATUS

approved

editing

#11 by Vaclav Kotesovec at Sun Apr 16 05:02:04 EDT 2017

STATUS

editing

approved

#10 by Vaclav Kotesovec at Sun Apr 16 05:00:35 EDT 2017

FORMULA

a(n) ~ exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / 4) * Zeta(3)^(1/6) / (2^(23/24) * 3^(1/3) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Apr 16 2017

#9 by Vaclav Kotesovec at Sun Apr 16 04:55:20 EDT 2017

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 + x^(4*k-3))^(4*k-3), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 16 2017 *)

STATUS

reviewed

editing

#8 by Joerg Arndt at Sun Apr 16 04:50:08 EDT 2017

STATUS

proposed

reviewed

#7 by Seiichi Manyama at Sun Apr 16 04:46:20 EDT 2017

STATUS

editing

proposed

#6 by Seiichi Manyama at Sun Apr 16 04:43:29 EDT 2017

FORMULA

a(n) = (-1)^n * A285070(n).

#5 by Seiichi Manyama at Sun Apr 16 04:40:35 EDT 2017

CROSSREFS

Product_{k>=0} (1 + x^(m*k+1))^(m*k+1): A262736 (m=2), A262949 (m=3), this sequence (m=4).