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A058484 McKay-Thompson series of class 12F for Monster. 4
1, 6, 21, 56, 126, 258, 498, 924, 1659, 2884, 4872, 8028, 12965, 20586, 32187, 49616, 75468, 113412, 168590, 248148, 361929, 523348, 750660, 1068576, 1510428, 2120934, 2959692, 4105808, 5663814, 7771452, 10609576, 14414676, 19494855, 26249984, 35197536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..148 from G. A. Edgar)

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

a(n) ~ exp(2*Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 10 2015

From G. A. Edgar, Mar 13 2017: (Start)

Expansion of q^(1/2)*(eta(q^2)*eta(q^3) / (eta(q)*eta(q^6)))^6 in powers of q.

T12F(q) = T6B(q^2)^(1/2) with T6B the g.f. of A121665, the convolution square of A058484. (End)

EXAMPLE

T12F = 1/q + 6*q + 21*q^3 + 56*q^5 + 126*q^7 + 258*q^9 + 498*q^11 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[((1+x^(3*k-1))*(1+x^(3*k-2)))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 10 2015 *)

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^3]/(eta[q]*eta[q^6]))^6; a := CoefficientList[Series[A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)

PROG

(PARI)q='q+O('q^66); Vec( eta(q^2)^6*eta(q^3)^6 / (eta(q)^6*eta(q^6)^6) )  \\ Joerg Arndt, Mar 13 2017

CROSSREFS

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

Sequence in context: A229886 A243740 A137361 * A145455 A145134 A256571

Adjacent sequences:  A058481 A058482 A058483 * A058485 A058486 A058487

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Vaclav Kotesovec, Sep 10 2015

STATUS

approved

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Last modified January 21 19:54 EST 2019. Contains 319350 sequences. (Running on oeis4.)