OFFSET
-1,3
COMMENTS
G.f. A(x) satisfies 0=f(A(x)+6,A(x^2)+6) where f(u,v)=(u+v)^3+uv(27+9(u+v)-uv). - Michael Somos, Jun 16 2004
Expansion of eta(q^3)^12/(eta(q)eta(q^9))^6-6 in powers of q.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, 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.
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
a(n) ~ exp(4*Pi*sqrt(n)/3) / (sqrt(6)*n^(3/4)). - Vaclav Kotesovec, May 01 2017
EXAMPLE
T9A = 1/q + 27*q + 86*q^2 + 243*q^3 + 594*q^4 + 1370*q^5 + 2916*q^6 + ...
MATHEMATICA
QP = QPochhammer; s = QP[q^3]^12/(QP[q]*QP[q^9])^6 - 6*q + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 13 2015, adapted from PARI *)
PROG
(PARI) a(n)=local(A); if(n<-1, 0, n++; A=x*O(x^n); polcoeff(eta(x^3+A)^12/(eta(x+A)*eta(x^9+A))^6-6*x, n)) /* Michael Somos, Jun 16 2004 */
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 28 1994
STATUS
approved