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A058758 McKay-Thompson series of class 84A for Monster. 1
1, 0, 1, 1, 1, 0, 3, 2, 2, 2, 2, 2, 5, 3, 6, 5, 7, 5, 10, 7, 11, 11, 13, 12, 19, 15, 21, 22, 26, 23, 35, 30, 39, 38, 47, 45, 60, 54, 68, 69, 81, 78, 104, 95, 117, 118, 137, 134, 171, 162, 192, 197, 225, 223, 274, 265, 313, 318, 363, 363, 434, 424, 494, 508, 570, 575, 675, 670, 765, 789, 884 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,7

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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of B + q/B, where B = q^(1/2)*(eta(q)*eta(q^6)*eta(q^14)* eta(q^21)/(eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42))), in powers of q. - G. C. Greubel, Jun 30 2018

a(n) ~ exp(2*Pi*sqrt(n/21)) / (2 * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T84A = 1/q + q^3 + q^5 + q^7 + 3*q^11 + 2*q^13 + 2*q^15 + 2*q^17 + 2*q^19 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; B:= q^(1/2)*(eta[q]*eta[q^6]* eta[q^14]*eta[q^21]/(eta[q^2]*eta[q^3]*eta[q^7]*eta[q^42])); a:= CoefficientList[Series[B + q/B , {q, 0, 60}], q];  Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 30 2018 *)

PROG

(PARI) q='q+O('q^50); B = (eta(q)*eta(q^6)*eta(q^14)*eta(q^21)/( eta(q^2) *eta(q^3)*eta(q^7)*eta(q^42))); Vec(B + q/B) \\ G. C. Greubel, Jun 30 2018

CROSSREFS

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

Sequence in context: A119704 A104223 A057934 * A122396 A272893 A037199

Adjacent sequences:  A058755 A058756 A058757 * A058759 A058760 A058761

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 30 2018

STATUS

approved

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Last modified January 17 16:53 EST 2019. Contains 319235 sequences. (Running on oeis4.)