The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A128517 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A128517

McKay-Thompson series of class 18E for the Monster group with a(0) = 3.
(history; published version)

#16 by Charles R Greathouse IV at Fri Mar 12 22:24:44 EST 2021

LINKS

M. Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>

Discussion

Fri Mar 12

22:24

OEIS Server: https://oeis.org/edit/global/2897

#15 by N. J. A. Sloane at Wed Nov 13 21:58:47 EST 2019

LINKS

M. Somos, <a href="http://somos.crg4.comA010815/multiqa010815.htmltxt">Introduction to Ramanujan theta functions</a>

Discussion

Wed Nov 13

21:58

OEIS Server: https://oeis.org/edit/global/2832

#14 by Alois P. Heinz at Sat Jun 16 17:36:46 EDT 2018

STATUS

proposed

approved

#13 by G. C. Greubel at Sat Jun 16 17:22:41 EDT 2018

STATUS

editing

proposed

#12 by G. C. Greubel at Sat Jun 16 17:22:34 EDT 2018

LINKS

G. C. Greubel, <a href="/A128517/b128517.txt">Table of n, a(n) for n = -1..1000</a>

STATUS

approved

editing

#11 by Vaclav Kotesovec at Tue Oct 13 06:26:00 EDT 2015

STATUS

editing

approved

#10 by Vaclav Kotesovec at Tue Oct 13 06:25:49 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

FORMULA

a(n) ~ exp(2*Pi*sqrt(2*n)/3) / (2^(3/4) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Oct 13 2015

#9 by Vaclav Kotesovec at Tue Oct 13 06:24:27 EDT 2015

MATHEMATICA

nmax=60; CoefficientList[Series[Product[((1+x^k) / (1+x^(9*k)))^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 13 2015 *)

STATUS

approved

editing

#8 by Michael Somos at Sun Apr 26 12:21:06 EDT 2015

STATUS

editing

approved

#7 by Michael Somos at Sun Apr 26 12:20:58 EDT 2015

PROG

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^9 + A) / (eta(x + A) * eta(x^18 + A)))^3, n))};

STATUS

approved

editing

Discussion

Sun Apr 26

12:21

Michael Somos: Light edit.