A058616 - OEIS

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A058616

McKay-Thompson series of class 30E for Monster.

1, 2, 3, 6, 9, 12, 18, 26, 34, 48, 66, 86, 115, 152, 196, 252, 324, 410, 518, 652, 815, 1016, 1260, 1556, 1914, 2344, 2860, 3482, 4222, 5104, 6160, 7408, 8883, 10634, 12694, 15112, 17962, 21300, 25198, 29764, 35091, 41284, 48495, 56870, 66567, 77800, 90790, 105780, 123070, 142988

(list; graph; refs; listen; history; text; internal format)

OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..2500

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

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of q^(1/3)*(eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^2 in powers of q. - G. C. Greubel, Jun 23 2018

a(n) ~ exp(2*Pi*sqrt(2*n/15)) / (2^(3/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T30E = 1/q + 2*q^2 + 3*q^5 + 6*q^8 + 9*q^11 + 12*q^14 + 18*q^17 + 26*q^20 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/3)*(eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)

PROG

(PARI) q='q+O('q^50); Vec((eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^2) \\ G. C. Greubel, Jun 23 2018

CROSSREFS

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

Sequence in context: A176893 A144677 A309677 * A298435 A261539 A325552

Adjacent sequences: A058613 A058614 A058615 * A058617 A058618 A058619

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(8) onward added by G. C. Greubel, Jun 23 2018

STATUS

approved