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A116916 Expansion of q^(-1/8) * (eta(q)^3 + 3 * eta(q^9)^3) in powers of q^3. +0
4
1, 5, -7, 0, 0, -11, 0, 13, 0, 0, 0, 0, 17, 0, 0, -19, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, -43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0 (list; graph; listen)
OFFSET

0,2

FORMULA

a(5n+3)=a(5n+4)=0. a(25n+1)=5a(n).

Expansion of f(-q) * a(q) in powers of q where f() is a Ramnaujan theta function and a() is a cubic AGM function.

Expansion of f(-q)^3 + 3 * q * f(-q^9)^3 in powers of q^3 where f() is a Ramanujan theta function.

G.f.: Sum_{k} (-1)^k * (6*k+1) * x^(k * (3*k+1) / 2).

EXAMPLE

q + 5*q^25 - 7*q^49 - 11*q^121 + 13*q^169 + 17*q^289 - 19*q^361 +...

PROGRAM

(PARI) {a(n)=if(issquare(24*n+1, &n), n* kronecker(3, n)* kronecker(-3, n))}

(PARI) {a(n)=if(n<1, n==0, n*=3; polcoeff( eta(x+x*O(x^n))^3 +3*x*eta(x^9+O(x^n))^3, n))}

CROSSREFS

A010816(3*n) = a(n).

Sequence in context: A042721 A048658 A001111 this_sequence A133079 A080332 A134756

Adjacent sequences: A116913 A116914 A116915 this_sequence A116917 A116918 A116919

KEYWORD

sign

AUTHOR

Michael Somos, Feb 26 2006

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.


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