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A058678 McKay-Thompson series of class 42d for Monster. 1
1, 1, 2, 2, 4, 5, 7, 8, 12, 14, 20, 23, 31, 37, 47, 56, 71, 84, 104, 122, 151, 178, 215, 252, 303, 355, 423, 492, 582, 676, 795, 920, 1076, 1242, 1445, 1662, 1926, 2210, 2549, 2916, 3353, 3827, 4386, 4992, 5703, 6478, 7379, 8362, 9499, 10742, 12174, 13738, 15533, 17496, 19736, 22190, 24979 (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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of q^(1/2)*(eta(q^3)*eta(q^7)/(eta(q)*eta(q^21))) in powers of q. - G. C. Greubel, Jun 26 2018

a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

EXAMPLE

T42d = 1/q + q + 2*q^3 + 2*q^5 + 4*q^7 + 5*q^9 + 7*q^11 + 8*q^13 + 12*q^15 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q^3]*eta[q^7]/(eta[q]*eta[q^21])), {q, 0, 60}], q]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jun 26 2018 *)

PROG

(PARI) q='q+O('q^60); Vec(eta(q^3)*eta(q^7)/(eta(q)*eta(q^21))) \\ G. C. Greubel, Jun 26 2018

CROSSREFS

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

Sequence in context: A120326 A036406 A029007 * A241410 A283106 A030739

Adjacent sequences:  A058675 A058676 A058677 * A058679 A058680 A058681

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 26 2018

STATUS

approved

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Last modified January 17 18:48 EST 2019. Contains 319251 sequences. (Running on oeis4.)