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A058726 McKay-Thompson series of class 60B for Monster. 2
1, 0, 0, 2, 2, 2, 3, 2, 5, 6, 5, 6, 9, 10, 10, 16, 17, 18, 25, 26, 31, 38, 37, 48, 60, 62, 68, 84, 95, 104, 125, 134, 154, 182, 192, 220, 257, 274, 309, 360, 394, 434, 492, 544, 607, 688, 740, 824, 944, 1018, 1123, 1266, 1377, 1524, 1697, 1850, 2041, 2264 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,4

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).

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Index entries for McKay-Thompson series for Monster simple group

FORMULA

a(n) ~ exp(2*Pi*sqrt(n/15)) / (2*15^(1/4)*n^(3/4)). - Vaclav Kotesovec, Jun 06 2018

Expansion of -1 + (eta(q^2)*eta(q^6)*eta(q^10)*eta(q^30))^2/(eta(q)* eta(q^3)*eta(q^4)*eta(q^5)*eta(q^12)*eta(q^15)*eta(q^20)*eta(q^60)) in powers of q. - G. C. Greubel, Jun 28 2018

EXAMPLE

T60B = 1/q + 2*q^2 + 2*q^3 + 2*q^4 + 3*q^5 + 2*q^6 + 5*q^7 + 6*q^8 + 5*q^9 + ...

MATHEMATICA

nmax = 60; CoefficientList[Series[-x + 1/Product[(1 + x^(2*k))*(1 + x^(6*k))*(1 + x^(10*k))*(1 + x^(30*k))*(1 - x^(2*k - 1))*(1 - x^(6*k - 3))*(1 - x^(10*k - 5))*(1 - x^(30*k - 15)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 06 2018 *)

eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^2]*eta[q^6]*eta[q^10]* eta[q^30])^2/(eta[q]*eta[q^3]*eta[q^4]*eta[q^5]*eta[q^12]*eta[q^15]* eta[q^20]*eta[q^60]); a:= CoefficientList[Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 28 2018 *)

PROG

(PARI) q='q+O('q^50); A = -1 + (eta(q^2)*eta(q^6)*eta(q^10)* eta(q^30))^2/(eta(q)*eta(q^3)*eta(q^4)*eta(q^5)*eta(q^12)*eta(q^15) *eta(q^20) *eta(q^60))/q; Vec(A) \\ G. C. Greubel, Jun 28 2018

CROSSREFS

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

Sequence in context: A104239 A283751 A132321 * A058614 A122765 A131053

Adjacent sequences:  A058723 A058724 A058725 * A058727 A058728 A058729

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 24 2014

STATUS

approved

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Last modified January 16 03:17 EST 2019. Contains 319184 sequences. (Running on oeis4.)