OFFSET
-1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = -1..1000
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
N. D. Elkies, Elliptic and modular curves over finite fields and related computational issues, in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 38.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.
FORMULA
Expansion of 9 + (eta(q) / eta(q^3))^12 in powers of q.
EXAMPLE
G.f. = 1/q - 3 + 54*q - 76*q^2 - 243*q^3 + 1188*q^4 - 1384*q^5 - 2916*q^6 + ...
MATHEMATICA
a[ n_] := With[{m = n + 1}, SeriesCoefficient[ 9 q + (Product[ 1 - q^k, {k, m}] / Product[ 1 - q^k, {k, 3, m, 3}])^12, {q, 0, m}]] (* Michael Somos, Nov 08 2011 *)
QP = QPochhammer; s = 9*q+(QP[q]/QP[q^3])^12 + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 12 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( 9*x + (eta(x + A) / eta(x^3 + A))^12, n))}; /* Michael Somos, Nov 08 2011 */
CROSSREFS
KEYWORD
sign,easy,nice
AUTHOR
STATUS
approved