The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A134786

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A134786

McKay-Thompson series of class 4A for the Monster group with a(0) = 4.
(history; published version)

#31 by Bruno Berselli at Wed Jan 24 09:08:48 EST 2018

STATUS

reviewed

#30 by Paolo P. Lava at Wed Jan 24 08:57:12 EST 2018

STATUS

proposed

#29 by G. C. Greubel at Tue Jan 23 22:03:46 EST 2018

STATUS

editing

#28 by G. C. Greubel at Tue Jan 23 22:03:39 EST 2018

LINKS

STATUS

approved

#27 by Vaclav Kotesovec at Thu Sep 07 05:10:00 EDT 2017

STATUS

editing

#26 by Vaclav Kotesovec at Thu Sep 07 05:09:53 EDT 2017

FORMULA

STATUS

approved

#25 by Michael Somos at Tue Jan 10 13:14:11 EST 2017

STATUS

editing

#24 by Michael Somos at Tue Jan 10 13:13:41 EST 2017

MATHEMATICA

a[ n_] :=

SeriesCoefficient[ -20 + QPochhammer[ -q, q^2]^24 / q, {q, 0, n}]; (* Michael Somos, May 05 2016 *)

STATUS

approved

Discussion

Tue Jan 10

13:14

Michael Somos: Rejoined split line.

#23 by Michael Somos at Thu May 05 15:06:44 EDT 2016

STATUS

editing

#22 by Michael Somos at Thu May 05 15:06:23 EDT 2016

FORMULA

G.f. is Fourier series of a level 4 modular function. f(-1/ (4 t)) = f(t) where q = exp(2 Pi i t).

EXAMPLE

1/q + 4 + 276*q + 2048*q^2 + 11202*q^3 + 49152*q^4 + 184024*q^5 + ...

MATHEMATICA

PROG

(PARI) {a(n) = local(A); if( n<-1, 0, A = x^2 * O(x^n); A = ( eta(x + A) / eta(x^4 + A) )^8 / x; polcoeff( 12 + A + 256 / A, n))}

CROSSREFS

A107080(n) = a(n) unless n=0. Convolution with A030212 is A037219.

STATUS

approved

Discussion

Thu May 05

15:06

Michael Somos: Added more info. Light and space edits.