The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A261389 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A261389

Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(3*k).
(history; published version)

#13 by Bruno Berselli at Mon Jan 30 02:52:30 EST 2017

STATUS

proposed

approved

#12 by G. C. Greubel at Sun Jan 29 22:32:41 EST 2017

STATUS

editing

proposed

#11 by G. C. Greubel at Sun Jan 29 22:32:21 EST 2017

LINKS

G. C. Greubel, <a href="/A261389/b261389.txt">Table of n, a(n) for n = 0..1000</a>

STATUS

approved

editing

#10 by Vaclav Kotesovec at Thu Oct 01 02:06:09 EDT 2015

STATUS

editing

approved

#9 by Vaclav Kotesovec at Thu Oct 01 02:06:05 EDT 2015

LINKS

Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 19.

STATUS

approved

editing

#8 by Vaclav Kotesovec at Mon Aug 17 17:46:46 EDT 2015

STATUS

editing

approved

#7 by Vaclav Kotesovec at Mon Aug 17 17:46:26 EDT 2015

COMMENTS

Convolution of A255610 and A027346.

CROSSREFS

Cf. A015128, A027346, A027906, A193427, A255610.

STATUS

approved

editing

#6 by Vaclav Kotesovec at Mon Aug 17 17:37:42 EDT 2015

STATUS

editing

approved

#5 by Vaclav Kotesovec at Mon Aug 17 17:29:46 EDT 2015

CROSSREFS

Cf. A015128, A156616, (t=1), A261386 (t=2).

Cf. A015128, A027906, A193427.

#4 by Vaclav Kotesovec at Mon Aug 17 17:25:19 EDT 2015

COMMENTS

In general, if g.f. = Product_{k>=1} ((1+x^k)/(1-x^k))^(t*k) and t>=1, then a(n) ~ exp(t/12 + 3/2 * (7*t*Zeta(3)/2)^(1/3) * n^(2/3)) * t^(1/6 + t/36) * (7*Zeta(3))^(1/6 + t/36) / (A^t * 2^(2/3 + t/9) * sqrt(3*Pi) * n^(2/3 + t/36)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.