A109063 Expansion of eta(q)/eta(q^5)^5 in powers of q.

1, -1, -1, 0, 0, 6, -5, -4, 0, 0, 25, -20, -16, 0, 0, 84, -65, -50, 0, 0, 250, -190, -144, 0, 0, 676, -505, -376, 0, 0, 1706, -1260, -929, 0, 0, 4064, -2970, -2166, 0, 0, 9243, -6700, -4850, 0, 0, 20200, -14535, -10444, 0, 0, 42677, -30520, -21802, 0, 0, 87512, -62235, -44212, 0, 0, 174814

Offset

-1,6

Links

Seiichi Manyama, Table of n, a(n) for n = -1..10000

W. Duke, Continued fractions and modular functions, Bull. Amer. Math. Soc. 42 (2005), 137-162. See page 150.

Formula

Euler transform of period 5 sequence [ -1, -1, -1, -1, 4, ...].

G.f. A(x) satisfies: 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=u^2*w^2 +2*u*v^2*w +4*u*v^3 -v^3*w.

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

a(5n+2) = a(5n+3) = 0.

Example

1/q -1 -q + 6*q^4 -5*q^5 -4*q^6 + 25*q^9 -20*q^10 -16*q^11 +...

Mathematica

QP:= QPochhammer; Table[SeriesCoefficient[QP[q]/QP[q^5]^5, {q, 0, n}], {n, 0, 50}] (* G. C. Greubel, Dec 13 2017 *)

Prog

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

Crossrefs

Cf. A053723.

Sequence in context: A193211 A195713 A306712 * A110390 A193178 A084448

Adjacent sequences: A109060 A109061 A109062 * A109064 A109065 A109066

Keyword

sign

Author

Michael Somos, Jun 17 2005

Status

approved