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A058640 McKay-Thompson series of class 35A for Monster. 2
1, 0, 1, 4, 6, 6, 10, 10, 19, 22, 32, 40, 51, 68, 86, 108, 135, 166, 218, 258, 325, 390, 477, 582, 713, 856, 1025, 1222, 1480, 1750, 2093, 2470, 2930, 3458, 4081, 4782, 5620, 6550, 7702, 8960, 10441, 12110, 14062, 16298, 18863, 21776, 25130, 28884, 33310 (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

Expansion of A - 1 - 1/A, where A = eta(q^5)*eta(q^7)/(eta(q)*eta(q^35)), in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ exp(4*Pi*sqrt(n/35)) / (sqrt(2) * 35^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T35A = 1/q + q + 4*q^2 + 6*q^3 + 6*q^4 + 10*q^5 + 10*q^6 + 19*q^7 + 22*q^8 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= eta[q^5]*eta[q^7]/( eta[q]* eta[q^35]); a:= CoefficientList[Series[q*(A - 1 - 1/A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q^5)*eta(q^7)/(q*eta(q)*eta(q^35)); Vec(A - 1 - 1/A) \\ G. C. Greubel, Jun 24 2018

CROSSREFS

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

Sequence in context: A098350 A276269 A163173 * A075653 A075656 A267573

Adjacent sequences:  A058637 A058638 A058639 * A058641 A058642 A058643

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 20 2014

STATUS

approved

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)