Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A132130
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A132130 McKay-Thompson series of class 10D for the Monster group with a(0) = 6. +0
2
1, 6, 21, 62, 162, 378, 819, 1680, 3276, 6138, 11145, 19662, 33840, 57048, 94362, 153432, 245757, 388218, 605466, 933414, 1423614, 2149586, 3215844, 4769544, 7016572, 10243896, 14848809, 21378276, 30582360, 43484304, 61473438, 86428896 (list; graph; listen)
OFFSET

-1,2

FORMULA

Euler transform of period 10 sequence [ 6, 0, 6, 0, 0, 0, 6, 0, 6, 0, ...].

G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= (v -u^2)*(v -w^2) -u*w* (12*(1+v^2) -20*v).

G.f. is Fourier series of a weight 0 level 10 modular form. f(-1/ ( 10 t)) = f(t) where q = exp(2 pi i t).

G.f.: x^(-1)* (Product_{k>0} (1+x^k)/ (1+x^(5*k)))^6.

G.f.: 1 / ( x * Product_{k>0} P(10,x^k)^6 ) where P(n,x) is the nth cyclotomic polynomial.

Expansion of q^(-1) * (chi(-q^5) / chi(-q))^6 in powers of q where chi() is a Ramanujan theta function.

Expansion of (eta(q^2) * eta(q^5) / (eta(q) * eta(q^10)))^6 in powers of q.

EXAMPLE

1/q + 6 + 21*q + 62*q^2 + 162*q^3 + 378*q^4 + 819*q^5 + 1680*q^6 + ...

PROGRAM

(PARI) {a(n)= local(A); if(n<-1, 0, n++; A= x*O(x^n); polcoeff( (eta(x^2+A)* eta(x^5+A)/ eta(x+A)/ eta(x^10+A))^6, n))}

CROSSREFS

A058100(n)= a(n) unless n=0.

Sequence in context: A012593 A048476 A122678 this_sequence A022571 A117962 A105457

Adjacent sequences: A132127 A132128 A132129 this_sequence A132131 A132132 A132133

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 11 2007, Aug 09 2008

EXTENSIONS

Edited by njas, May 16 2008 at the suggestion of R. J. Mathar

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified December 3 01:16 EST 2008. Contains 151161 sequences.


AT&T Labs Research