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A007266 McKay-Thompson series of class 9A for Monster.
(Formerly M5192)
2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=-1..28.

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.

Index entries for McKay-Thompson series for Monster simple group

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-Fran├žois 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

Adjacent sequences:  A007263 A007264 A007265 * A007267 A007268 A007269

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 28 1994

STATUS

approved

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Last modified December 8 11:15 EST 2016. Contains 278939 sequences.