The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A007249 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A007249

McKay-Thompson series of class 4D for the Monster group.
(history; published version)

#49 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

#48 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

#47 by Susanna Cuyler at Wed Feb 14 08:24:36 EST 2018

STATUS

proposed

approved

#46 by Michel Marcus at Wed Feb 14 01:29:47 EST 2018

STATUS

editing

proposed

#45 by Michel Marcus at Wed Feb 14 01:29:42 EST 2018

MATHEMATICA

eta[q_]:=q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/2)*(eta[q]/eta[q^2])^12, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Feb 13 2018 *)

STATUS

proposed

editing

#44 by G. C. Greubel at Tue Feb 13 21:27:15 EST 2018

STATUS

editing

proposed

#43 by G. C. Greubel at Tue Feb 13 21:26:12 EST 2018

COMMENTS

The convolution square root of A007191, and also the left and right borders of the triangle A161196. [- _Gary W. Adamson, _, Jun 06 2009]

FORMULA

Expansion of q^(1/2)*(eta(q)/eta(q^2))^12 in powers of q. - G. C. Greubel, Feb 13 2018

MATHEMATICA

eta[q_]:=q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/2)*(eta[q]/eta[q^2])^12, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* _G. C.Greubel_, Feb 13 2018 *)

STATUS

approved

editing

#42 by Alois P. Heinz at Tue Feb 06 15:06:21 EST 2018

STATUS

proposed

approved

#41 by Ilya Gutkovskiy at Tue Feb 06 14:57:40 EST 2018

STATUS

editing

proposed

#40 by Ilya Gutkovskiy at Tue Feb 06 14:39:37 EST 2018

FORMULA

G.f.: prod(Product_{m>=1, } (1 + x^m )^(-12).

G.f.: exp(-12*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018

CROSSREFS

Column k=12 of A286352.

STATUS

approved

editing