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A058606 McKay-Thompson series of class 28A for Monster. 1
1, 3, 1, 7, 7, 18, 18, 35, 38, 65, 71, 119, 140, 207, 240, 356, 409, 581, 679, 946, 1100, 1493, 1738, 2307, 2704, 3528, 4134, 5314, 6221, 7907, 9233, 11613, 13566, 16907, 19700, 24336, 28350, 34716, 40379, 49140, 57090, 68991, 80021, 96188, 111357, 133156, 153923, 183194, 211422 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of A + q/A, where A = q^(1/2)*((eta(q^2)*eta(q^7))/(eta(q) *eta(q^14)))^2, in powers of q. - G. C. Greubel, Jun 18 2018

a(n) ~ exp(2*Pi*sqrt(n/7)) / (2 * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T28A = 1/q + 3*q + q^3 + 7*q^5 + 7*q^7 + 18*q^9 + 18*q^11 + 35*q^13 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; e28D:= q^(1/2)*((eta[q^2]*eta[q^7])/(eta[q]*eta[q^14]))^2; a[n_]:= SeriesCoefficient[e28D + q/e28D, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 18 2018 *)

PROG

(PARI) q='q+O('q^50); A = ((eta(q^2)*eta(q^7))/(eta(q) *eta(q^14)))^2; Vec(A + q/A) \\ G. C. Greubel, Jun 18 2018

CROSSREFS

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A188463 A319298 A101748 * A135284 A016647 A091039

Adjacent sequences:  A058603 A058604 A058605 * A058607 A058608 A058609

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Feb 18 2018

STATUS

approved

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Last modified January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)