login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002507 Expansion of a modular function for Gamma_0(6).
(Formerly M1542 N0602)
12

%I M1542 N0602 #30 Dec 20 2021 20:25:56

%S 1,2,-5,-24,-23,76,249,168,-599,-1670,-1026,3272,8529,5232,-14062,

%T -35976,-22337,51516,131617,82568,-169376,-432636,-273332,513584,

%U 1309800,830372,-1456569,-3709672,-2354215,3904696,9931407,6301120,-9983208,-25339626,-16057040,24504584,62033318

%N Expansion of a modular function for Gamma_0(6).

%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A002507/b002507.txt">Table of n, a(n) for n = -3..10000</a>

%H Morris Newman, <a href="http://plms.oxfordjournals.org/content/s3-9/3/373.extract">Construction and application of a class of modular functions (II)</a>. Proc. London Math. Soc. (3) 9 1959 373-387.

%H Morris Newman, <a href="/A002507/a002507.pdf">Construction and application of a class of modular functions, II</a>, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]

%F Expansion of q^-3 * psi(q)^6 * phi(-q)^2 in powers of q where phi(), psi() are Ramanujan theta functions. - _Michael Somos_, Apr 24 2014

%F Expansion of eta(q^2)^10 * eta(q^3)^14 / (eta(q)^2 * eta(q^6)^22) in powers of q.

%F Euler transform of period 6 sequence [2, -8, -12, -8, 2, 0, ...]. - _Michael Somos_, Nov 10 2005

%F Convolution product of A128632, A128633, and A105559 (all three of them are modular functions and McKay-Thompson series of class 6E for the monster group). - _Michael Somos_, May 23 2014

%e G.f. = q^-3 + 2*q^-2 - 5*q^-1 - 24 - 23*q + 76*q^2 + 249*q^3 + 168*q^4 + ...

%t QP = QPochhammer; s = QP[q^2]^10*(QP[q^3]^14/(QP[q]^2*QP[q^6]^22)) + O[q]^40; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 14 2015, adapted from PARI *)

%o (PARI) {a(n) = local(A); if( n<-3, 0, n+=3; A = x * O(x^n); polcoeff( eta(x^2 + A)^10 * eta(x^3 + A)^14 / (eta(x + A)^2 * eta(x^6 + A)^22), n))}; /* _Michael Somos_, Nov 10 2005 */

%Y Cf. A002508, A105559, A128632, A128633.

%K sign,easy

%O -3,2

%A _N. J. A. Sloane_

%E More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 03:41 EDT 2024. Contains 371264 sequences. (Running on oeis4.)