login
A186210
Coefficients of modular function denoted G_5(tau) by Atkin.
1
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
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
KEYWORD
sign
AUTHOR
Michael Somos, Feb 15 2011
STATUS
approved