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A058754 McKay-Thompson series of class 78A for Monster. 1
1, 0, 1, 1, 1, 0, 2, 1, 3, 3, 3, 2, 6, 4, 6, 6, 8, 6, 11, 9, 13, 14, 16, 14, 24, 19, 27, 27, 33, 30, 43, 38, 51, 51, 61, 58, 79, 72, 92, 94, 110, 106, 138, 130, 160, 164, 189, 188, 235, 226, 270, 279, 321, 320, 388, 381, 448, 462, 525, 530, 631, 626, 724, 750 (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, 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^6)*eta(q^26)*eta(q^39)/( eta(q^2)*eta(q^3)*eta(q^13)*eta(q^78)), in powers of q. - G. C. Greubel, Jun 30 2018

a(n) ~ exp(2*Pi*sqrt(2*n/39)) / (2^(3/4) * 39^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T78A = 1/q + q + q^2 + q^3 + 2*q^5 + q^6 + 3*q^7 + 3*q^8 + 3*q^9 + 2*q^10 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; B:= eta[q]*eta[q^6]*eta[q^26]* eta[q^39]/(eta[q^2]*eta[q^3]*eta[q^13]*eta[q^78]);  a:= CoefficientList[ Series[1 + B + 1/B, {q, 0, 60}], q]; Table[[[n]], {n, 1, 50}]  (* G. C. Greubel, Jun 30 2018 *)

PROG

(PARI) q='q+O('q^50); B = eta(q)*eta(q^6)*eta(q^26)*eta(q^39)/(q*eta(q^2) *eta(q^3)*eta(q^13)*eta(q^78)); Vec(B + 1 + 1/B) \\ G. C. Greubel, Jun 30 2018

CROSSREFS

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

Sequence in context: A113278 A132382 A048865 * A279909 A125087 A271373

Adjacent sequences:  A058751 A058752 A058753 * A058755 A058756 A058757

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 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)