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A045489 McKay-Thompson series of class 7A for the Monster group with a(0) = 3. 4
1, 3, 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

-1,2

LINKS

G. C. Greubel, 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. 66.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. 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 -7 + (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, Sep 07 2017

EXAMPLE

1/q + 3 + 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 - 7*q + q*((1+7*h)^2/h - 1/q) + O[q]^30; CoefficientList[s, q] (* Jean-Fran├žois Alcover, Nov 15 2015 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; h:= (eta[q]/eta[q^7])^4; A045489 := CoefficientList[Series[q*(h + 7 + 49/h), {q, 0, 50}], q]; Table[ A045489[[n]], {n, 1, 30}] (* G. C. Greubel, May 28 2018 *)

PROG

(PARI) q='q+O('q^30); {h =(eta(q)/eta(q^7))^4/q};  Vec(h + 7 + 49/h) \\ G. C. Greubel, May 28 2018

CROSSREFS

Essentially same as A007264 and A030183.

Sequence in context: A316645 A116630 A317455 * A232453 A248341 A145242

Adjacent sequences:  A045486 A045487 A045488 * A045490 A045491 A045492

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 16 03:30 EST 2019. Contains 319184 sequences. (Running on oeis4.)