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A058741 McKay-Thompson series of class 66a for Monster. 1
1, 0, 1, 2, 2, 1, 3, 2, 3, 5, 5, 5, 8, 7, 10, 13, 12, 14, 19, 19, 23, 28, 31, 33, 43, 43, 51, 60, 65, 71, 87, 91, 104, 121, 130, 144, 171, 180, 202, 232, 250, 274, 318, 338, 378, 426, 461, 506, 575, 613, 680, 759, 821, 897, 1007, 1080, 1187, 1316, 1423, 1550, 1721, 1847, 2022, 2226 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,4

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1499

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 sqrt(T33B) in powers of q, where T33B = A058637. - G. C. Greubel, Jul 03 2018

a(n) ~ exp(2*Pi*sqrt(2*n/33)) / (2^(3/4) * 33^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 05 2018

EXAMPLE

T66a = 1/q + q^3 + 2*q^5 + 2*q^7 + q^9 + 3*q^11 + 2*q^13 + 3*q^15 + 5*q^17 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A := eta[q]*eta[q^11]/ (eta[q^3]*eta[q^33]); a:= CoefficientList[Series[ (q*(1 + A + 3/A) + O[q]^nmax)^(1/2), {q, 0, 90}], q]; Table[a[[n]], {n, 1, 80}]  (* G. C. Greubel, Jul 03 2018 *)

PROG

(PARI) q='q+O('q^80); A = eta(q)*eta(q^11)/(q*eta(q^3)*eta(q^33)); Vec(sqrt(q*(A + 1 + 3/A))) \\ G. C. Greubel, Jul 03 2018

CROSSREFS

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

Sequence in context: A289438 A008678 A159803 * A291712 A074945 A276427

Adjacent sequences:  A058738 A058739 A058740 * A058742 A058743 A058744

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jul 03 2018

STATUS

approved

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Last modified January 20 17:05 EST 2019. Contains 319335 sequences. (Running on oeis4.)