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
KEYWORD
sign
AUTHOR
Michael Somos, Feb 15 2011
STATUS
approved