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URL: https://oeis.org/A007266

⇱ A007266 - OEIS

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A007266
McKay-Thompson series of class 9A for Monster.
3
1, 0, 27, 86, 243, 594, 1370, 2916, 5967, 11586, 21870, 39852, 71052, 123444, 210654, 352480, 581013, 942786, 1510254, 2388204, 3734964, 5777788, 8852004, 13434984, 20218395, 30177684, 44704413, 65743348, 96033357, 139368816
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
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
Cf. A045491.
Sequence in context: A260052 A028993 A262367 * A098320 A034990 A090949
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 28 1994
STATUS
approved