A186210 Coefficients of modular function denoted G_5(tau) by Atkin.

1, -12, 54, -88, -99, 540, -418, -648, 594, 836, 1056, -4092, -353, 4752, -1650, 3068, 0, -9768, -8074, 12144, 27258, 572, -54504, -4884, 45045, -22176, 61656, 0, -104676, -69564, 78914, 290664, -72732, -411180, 8646, 241812, -117194, 567996, 0

Offset

-5,2

Links

G. C. Greubel, Table of n, a(n) for n = -5..2500

A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J., 8 (1967), 14-32.

Formula

Convolution inverse of g_5(tau) (A186209).

Expansion of (eta(q) / eta(q^11))^12 in powers of q.

Euler transform of period 11 sequence [-12, -12, -12, -12, -12, -12, -12, -12, -12, -12, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (11 t)) = 11^6 / f(t) where q = exp(2 Pi i t).

G.f.: x^-5 * (Product_{k>0} (1 - x^k) / (1 - x^(11*k)))^12.

Example

G.f. = q^-5 - 12*q^-4 + 54*q^-3 - 88*q^-2 - 99*q^-1 + 540 - 418*q - 648*q^2 + ...

Mathematica

QP = QPochhammer; s = (QP[q]/QP[q^11])^12 + O[q]^50; CoefficientList[s, q] (* Jean-François Alcover, Nov 14 2015, adapted from PARI *)

Prog

(PARI) {a(n) = my(A); if( n<-5, 0, n+=5; A = x * O(x^n); polcoeff( (eta(x^1 + A) / eta(x^11 + A))^12, n))};

Crossrefs

Cf. A186209.

Sequence in context: A060171 A133078 A034436 * A209676 A000735 A341558

Adjacent sequences: A186207 A186208 A186209 * A186211 A186212 A186213

Keyword

sign

Author

Michael Somos, Feb 15 2011

Status

approved