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A131018 Expansion of (q^-3) *psi(q)/ psi(q^25) in powers of q where psi() is a Ramanujan theta function. +0
1
1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -2, -2, 0, 0, 0, -1, -2, 0, 0, 0, -2, 1, 0, 0, 0, -2, 0, 0, 0, 0, 1, -2, 0, 0, 0, 3, 3, 0, 0, 0 (list; graph; listen)
OFFSET

-3,76

REFERENCES

F. Calegari, Review of "A first Course in modular forms" by F. Diamond and J. Shurman, Bull. Amer. Math. Soc., 43 (No. 3, 2006), 415-421. See p. 418

FORMULA

G.f.: (x^-3) *Product_{k>0} (1-x^k) *(1+x^k)^2/ ((1-x^(25k)) *(1+x^(50k))^2).

EXAMPLE

q^-3 + q^-2 + 1 + q^3 + q^7 + q^12 + q^18 - q^22 - q^23 - q^28 + ...

PROGRAM

(PARI) {a(n)=local(A); if(n<-3, 0, n+=3; A=x*O(x^n); polcoeff( eta(x^2+A)^2 *eta(x^25+A)/ (eta(x+A) *eta(x^50+A)^2), n))}

CROSSREFS

Adjacent sequences: A131015 A131016 A131017 this_sequence A131019 A131020 A131021

Sequence in context: A037863 A113302 A049800 this_sequence A035395 A116856 A140344

KEYWORD

sign

AUTHOR

Michael Somos, Jun 10 2007

page 1

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Last modified October 7 14:39 EDT 2008. Contains 144666 sequences.


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