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A058744 McKay-Thompson series of class 70A for Monster. 2
1, 0, 1, 0, 2, 2, 2, 2, 3, 2, 4, 4, 7, 4, 10, 8, 11, 10, 14, 14, 21, 18, 25, 22, 33, 32, 41, 38, 52, 50, 65, 62, 82, 78, 101, 102, 124, 122, 150, 152, 189, 186, 230, 226, 279, 280, 334, 340, 402, 412, 487, 492, 582, 592, 697, 714, 831, 850, 980, 1014, 1173 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,5

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 B + 1 + 1/B, where B = eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/ (eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)), in powers of q. - 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, Jun 30 2018

EXAMPLE

T70A = 1/q + q + 2*q^3 + 2*q^4 + 2*q^5 + 2*q^6 + 3*q^7 + 2*q^8 + 4*q^9 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; B:= eta[q]*eta[q^10]*eta[q^14]* eta[q^35]/(eta[q^2]*eta[q^5]*eta[q^7]*eta[q^70]); a:= CoefficientList[ Series[1 + B + 1/B, {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)*eta(q^10)*eta(q^14)*eta(q^35)/ (q*eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)); Vec(B + 1 + 1/B) \\ G. C. Greubel, Jun 30 2018

CROSSREFS

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

Sequence in context: A029348 A070093 A174931 * A323246 A185617 A250268

Adjacent sequences:  A058741 A058742 A058743 * A058745 A058746 A058747

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 24 2014

STATUS

approved

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Last modified January 18 13:42 EST 2019. Contains 319271 sequences. (Running on oeis4.)