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A058535 McKay-Thompson series of class 18E for Monster. 2
1, 0, 6, 13, 24, 42, 73, 120, 192, 299, 456, 684, 1007, 1464, 2100, 2976, 4176, 5802, 7993, 10920, 14808, 19946, 26688, 35496, 46944, 61752, 80826, 105286, 136536, 176304, 226725, 290448, 370704, 471467, 597600, 755028, 950980, 1194216 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

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 + 2 + 6/A, where A = (eta(q)^2*eta(q^6)*eta(q^9)/(eta(q^2) *eta(q^3)*eta(q^18)^2)), in powers of q. - G. C. Greubel, Jun 18 2018

a(n) ~ exp(2*Pi*sqrt(2*n)/3) / (2^(3/4) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

EXAMPLE

T18E = 1/q + 6*q + 13*q^2 + 24*q^3 + 42*q^4 + 73*q^5 + 120*q^6 + 192*q^7 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; e18D3:= (eta[q]^2*eta[q^6]*eta[q^9]/( eta[q^2]*eta[q^3]*eta[q^18]^2)); a := CoefficientList[Series[2 + e18D3 + 6/e18D3, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q)^2*eta(q^6)*eta(q^9)/(eta(q^2)*eta(q^3) *eta(q^18)^2))/q; Vec(A + 2 + 6/A) \\ G. C. Greubel, Jun 18 2018

CROSSREFS

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

Cf. A128517 (same sequence except for n=0).

Sequence in context: A296310 A235450 A032528 * A131833 A101736 A162432

Adjacent sequences:  A058532 A058533 A058534 * A058536 A058537 A058538

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 19 2014

STATUS

approved

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Last modified October 21 06:36 EDT 2019. Contains 328292 sequences. (Running on oeis4.)