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A058637 McKay-Thompson series of class 33B for Monster. 2
1, 0, 2, 4, 5, 6, 14, 14, 20, 30, 37, 46, 71, 82, 108, 144, 173, 218, 291, 340, 425, 540, 647, 788, 996, 1170, 1427, 1744, 2072, 2476, 3019, 3536, 4224, 5058, 5942, 7008, 8363, 9734, 11453, 13512, 15719, 18340, 21546, 24908, 28983, 33774, 38995, 45086, 52353 (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 + 3/A, where A =eta(q)*eta(q^11)/(eta(q^3)*eta(q^33)), in powers of q. - G. C. Greubel, Jun 23 2018

a(n) ~ exp(4*Pi*sqrt(n/33)) / (sqrt(2) * 33^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T33B = 1/q + 2*q + 4*q^2 + 5*q^3 + 6*q^4 + 14*q^5 + 14*q^6 + 20*q^7 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := eta[q]*eta[q^11]/( eta[q^3]* eta[q^33]); a:= CoefficientList[Series[q*(A + 1 + 3/A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q)*eta(q^11)/(q*eta(q^3)*eta(q^33)); Vec(A + 1 + 3/A) \\ G. C. Greubel, Jun 23 2018

CROSSREFS

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

Sequence in context: A031150 A125775 A191165 * A026473 A272929 A008319

Adjacent sequences:  A058634 A058635 A058636 * A058638 A058639 A058640

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.)