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A058746 McKay-Thompson series of class 70a for Monster. 1
1, 1, 0, 2, 1, 2, 1, 2, 3, 4, 5, 5, 5, 7, 8, 11, 10, 13, 14, 16, 19, 22, 23, 28, 32, 37, 38, 45, 51, 58, 65, 73, 78, 91, 98, 114, 123, 136, 153, 170, 187, 206, 226, 255, 276, 312, 334, 369, 406, 448, 492, 538, 586, 646, 701, 773, 837, 917, 997, 1093, 1188, 1291, 1397, 1532, 1657, 1808 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,4

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 sqrt(2 + T35A) in powers of q, where T35A = A058640. - G. C. Greubel, Jun 30 2018

a(n) ~ exp(2*Pi*sqrt(2*n/35)) / (2^(3/4) * 35^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T70a = 1/q + q + 2*q^5 + q^7 + 2*q^9 + q^11 + 2*q^13 + 3*q^15 + 4*q^17 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 80; B:= eta[q^5]*eta[q^7]/( eta[q]*eta[q^35]); a:= CoefficientList[Series[(q (1 + B - 1/B + O[q]^nmax))^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 30 2018*)

PROG

(PARI) q='q+O('q^50); B = eta(q^5)*eta(q^7)/(q*eta(q)*eta(q^35)); Vec(sqrt(q*(B + 1 - 1/B))) \\ G. C. Greubel, Jul 01 2018

CROSSREFS

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

Sequence in context: A261273 A097454 A139803 * A080916 A071622 A182063

Adjacent sequences:  A058743 A058744 A058745 * A058747 A058748 A058749

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 20 16:44 EST 2019. Contains 319335 sequences. (Running on oeis4.)