|
| |
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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 A022704
Adjacent sequences: A186207 A186208 A186209 * A186211 A186212 A186213
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
Michael Somos, Feb 15 2011
|
|
|
STATUS
|
approved
|
| |
|
|
