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A058555 McKay-Thompson series of class 20F for Monster. 3
1, 0, 5, 10, 18, 30, 51, 80, 124, 190, 281, 410, 592, 840, 1178, 1640, 2253, 3070, 4154, 5570, 7422, 9830, 12932, 16920, 22028, 28520, 36761, 47180, 60280, 76720, 97278, 122880, 154693, 194110, 242776, 302740, 376424, 466710, 577114, 711800, 875707, 1074790 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..5000

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/5)) / (2*5^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 21 2018

Expansion of -2 + (eta(q^4)*eta(q^5)/(eta(q)*eta(q^20)))^2 in powers of q. - G. C. Greubel, Jun 14 2018

EXAMPLE

T20F = 1/q + 5*q + 10*q^2 + 18*q^3 + 30*q^4 + 51*q^5 + 80*q^6 + 124*q^7 + ...

MATHEMATICA

nmax = 50; QP=QPochhammer; CoefficientList[Series[-2*x + (QP[x^4] *QP[x^5]/(QP[x]*QP[x^20]))^2, {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 21 2018 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-2 + (eta[q^4]*eta[q^5]/(eta[q]*eta[q^20]))^2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)

PROG

(PARI) q='q+O('q^50); A= -2 + (eta(q^4)*eta(q^5)/(eta(q)*eta(q^20)))^2/q; Vec(A) \\ G. C. Greubel, Jun 14 2018

CROSSREFS

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

Sequence in context: A164004 A025010 A299144 * A226445 A296552 A251928

Adjacent sequences:  A058552 A058553 A058554 * A058556 A058557 A058558

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 January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)