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A109040 Expansion of 1-eta(q)eta(q^3)(eta(q^4)eta(q^6))^2/eta(q^12)^2 in powers of q. 1
1, 1, 1, 1, -4, 1, -6, 1, 1, -4, 12, 1, 14, -6, -4, 1, -16, 1, -18, -4, -6, 12, 24, 1, 21, 14, 1, -6, -28, -4, -30, 1, 12, -16, 24, 1, 38, -18, 14, -4, -40, -6, -42, 12, -4, 24, 48, 1, 43, 21, -16, 14, -52, 1, -48, -6, -18, -28, 60, -4, 62, -30, -6, 1, -56, 12, -66, -16, 24, 24, 72, 1, 74, 38, 21, -18, -72, 14, -78, -4, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

REFERENCES

N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 85, Eq. (32.68).

LINKS

Table of n, a(n) for n=1..81.

FORMULA

Multiplicative with a(2^e)=a(3^e)=1, a(p^e)=(p^(e+1)-1)/(p-1) if p = 1, 11 (mod 12), a(p^e)=((-p)^(e+1)-1)/(-p-1) if p = 5, 7 (mod 12).

G.f.: 1-Product_{k>0} (1-x^k)(1-x^(3k))(1-x^(4k))^2/(1+x^(6k))^2 = Sum_{k>0} x^k*(1-3*x^(2k)+x^(4k))*(1+x^(2k))^3/(1+x^(6k))^2.

PROG

(PARI) a(n)=if(n<1, 0, direuler(p=2, n, 1/(1-X)/(1-p*kronecker(12, p)*X))[n])

(PARI) {a(n)=local(A); if(n<1, 0, A=x*O(x^n); polcoeff( 1-eta(x+A)*eta(x^3+A)*eta(x^4+A)^2*eta(x^6+A)^2/eta(x^12+A)^2, n))}

CROSSREFS

Cf. A109039(n)=-a(n), if n>0.

Sequence in context: A176216 A109039 A257656 * A133828 A144907 A185093

Adjacent sequences:  A109037 A109038 A109039 * A109041 A109042 A109043

KEYWORD

sign,mult

AUTHOR

Michael Somos, Jun 17 2005

STATUS

approved

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Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)