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A058701 McKay-Thompson series of class 50A for Monster. 1
1, 0, 2, 1, 2, 2, 5, 4, 7, 7, 12, 10, 17, 16, 25, 24, 35, 34, 51, 49, 69, 70, 96, 96, 130, 132, 175, 180, 231, 240, 308, 320, 402, 423, 526, 552, 680, 718, 877, 928, 1120, 1190, 1430, 1520, 1809, 1932, 2285, 2440, 2870, 3072, 3594, 3850, 4477, 4802, 5565 (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).

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^2)*eta(q^25)/(eta(q)*eta(q^50) ), in powers of q. - G. C. Greubel, Jun 27 2018

a(n) ~ exp(2*Pi*sqrt(2*n)/5) / (2^(3/4) * sqrt(5) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T50A = 1/q + 2*q + q^2 + 2*q^3 + 2*q^4 + 5*q^5 + 4*q^6 + 7*q^7 + 7*q^8 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^2]*eta[q^25]/( eta[q]* eta[q^50])); a:= CoefficientList[Series[-1 + A + 1/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 27 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q^2)*eta(q^25)/(q*eta(q)*eta(q^50)); Vec(A - 1 + 1/A) \\ G. C. Greubel, Jun 27 2018

CROSSREFS

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

Sequence in context: A050315 A128978 A145862 * A004559 A214968 A095291

Adjacent sequences:  A058698 A058699 A058700 * A058702 A058703 A058704

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 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)