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A058714 McKay-Thompson series of class 56A for the Monster group. 1
1, 0, 1, 2, 1, 2, 3, 4, 5, 6, 8, 8, 10, 12, 15, 18, 22, 26, 29, 34, 39, 48, 55, 64, 76, 84, 97, 112, 128, 146, 168, 192, 217, 246, 277, 316, 355, 402, 454, 508, 572, 640, 721, 804, 898, 1008, 1119, 1248, 1392, 1548, 1718, 1910, 2118, 2344, 2598, 2872, 3181 (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, 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 -1 + eta(q^2)*eta(q^4)*eta(q^14)*eta(q^28)/(eta(q)*eta(q^7) *eta(q^8)*eta(q^56)) in powers of q. - G. C. Greubel, Jun 27 2018

a(n) ~ exp(sqrt(2*n/7)*Pi) / (2^(5/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T56A = 1/q + q + 2*q^2 + q^3 + 2*q^4 + 3*q^5 + 4*q^6 + 5*q^7 + 6*q^8 + 8*q^9 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q^2]*eta[q^4]*eta[q^14]* eta[q^28]/(eta[q]*eta[q^7]*eta[q^8]*eta[q^56])); a:= CoefficientList[ Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}]  (* G. C. Greubel, Jun 27 2018 *)

PROG

(PARI) q='q+O('q^50); Vec(-1 + eta(q^2)*eta(q^4)*eta(q^14)*eta(q^28)/(q* eta(q)*eta(q^7)*eta(q^8)*eta(q^56))) \\ G. C. Greubel, Jun 27 2018

CROSSREFS

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

Sequence in context: A137846 A080915 A239484 * A057045 A237753 A058700

Adjacent sequences:  A058711 A058712 A058713 * A058715 A058716 A058717

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 February 17 12:10 EST 2020. Contains 331996 sequences. (Running on oeis4.)