The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A007242 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A007242

McKay-Thompson series of class 2a for the Monster group.
(history; published version)

#89 by Charles R Greathouse IV at Fri Mar 12 22:24:41 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

#88 by N. J. A. Sloane at Sun Feb 14 01:15:58 EST 2021

STATUS

editing

approved

#87 by N. J. A. Sloane at Sun Feb 14 01:15:56 EST 2021

LINKS

Masao Koike, <a href="https://oeis.org/A004016/a004016.pdf">Modular forms on non-compact arithmetic triangle groups</a>, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021. I wrote 2005 on the first page but the internal evidence suggests 1997.]

STATUS

approved

editing

#86 by N. J. A. Sloane at Wed Nov 13 21:54:12 EST 2019

LINKS

M. Somos, <a href="http://cis.csuohio.edu/~somosA010815/multiqa010815.pdftxt">Introduction to Ramanujan theta functions</a>

Discussion

Wed Nov 13

21:54

OEIS Server: https://oeis.org/edit/global/2830

#85 by Susanna Cuyler at Wed May 09 22:58:07 EDT 2018

STATUS

proposed

approved

#84 by G. C. Greubel at Wed May 09 21:35:09 EDT 2018

STATUS

editing

proposed

#83 by G. C. Greubel at Wed May 09 21:34:51 EDT 2018

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 55; f1A := (eta[q]/eta[q^2] )^24*(1 +256*(eta[q^2]/eta[q])^24)^3; A007242:= CoefficientList[ Series[(q*f1A - 1728*q + O[q]^nmax)^(1/2), {q, 0, 50}], q]; Table[ A007242[[n]], {n, 1, 50}] (* G. C. Greubel, May 09 2018 *)

STATUS

approved

editing

#82 by Vaclav Kotesovec at Sun Jul 09 06:46:54 EDT 2017

STATUS

editing

approved

#81 by Vaclav Kotesovec at Sun Jul 09 06:46:43 EDT 2017

FORMULA

a(n) ~ -exp(2*Pi*sqrt(2*n)) / (2^(3/4) * n^(3/4)). - Vaclav Kotesovec, Jul 09 2017

STATUS

approved

editing

#80 by OEIS Server at Sun Jul 02 21:55:12 EDT 2017

LINKS

Seiichi Manyama, <a href="/A007242/b007242_1.txt">Table of n, a(n) for n = 0..5000</a> (terms 0..500 from G. A. Edgar)