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A058616 McKay-Thompson series of class 30E for Monster. 1
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: A008810 A176893 A144677 * A298435 A261539 A271882

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

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)