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A007264 McKay-Thompson series of class 7A for Monster.
(Formerly M5302)
4
1, 0, 51, 204, 681, 1956, 5135, 12360, 28119, 60572, 125682, 251040, 487426, 920568, 1699611, 3070508, 5445510, 9490116, 16283793, 27537708, 45959775, 75760640, 123471327, 199081632, 317814988 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Seiichi Manyama, Table of n, a(n) for n = -1..10000

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. 39.

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

FORMULA

Expansion of (h+7)^2/h, where h = (eta(q)/eta(q^7))^4.

a(n) ~ exp(4*Pi*sqrt(n/7)) / (sqrt(2) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Dec 04 2015

EXAMPLE

T7A = 1/q + 51*q + 204*q^2 + 681*q^3 + 1956*q^4 + 5135*q^5 + 12360*q^6 + ...

MATHEMATICA

QP = QPochhammer; h = q*(QP[q^7]/QP[q])^4; s = 1 - 10*q + q*((1+7*h)^2/h - 1/q) + O[q]^30; CoefficientList[s, q] (* Jean-Fran├žois Alcover, Nov 15 2015 *)

PROG

(PARI) q='q+O('q^50); F =(eta(q)/eta(q^7))^4/q;  Vec(F*(1 + 7/F)^2 - 10) \\ G. C. Greubel, May 10 2018

CROSSREFS

Essentially same as A045489 and A030183.

Sequence in context: A031431 A157365 A157916 * A158640 A107253 A030535

Adjacent sequences:  A007261 A007262 A007263 * A007265 A007266 A007267

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 20 02:35 EDT 2019. Contains 328244 sequences. (Running on oeis4.)