A058675 McKay-Thompson series of class 42a for Monster.

1, 0, 3, 3, 3, 6, 7, 6, 12, 16, 18, 24, 33, 33, 48, 57, 69, 87, 106, 117, 153, 181, 207, 258, 307, 345, 429, 496, 570, 681, 805, 906, 1083, 1252, 1425, 1671, 1934, 2190, 2562, 2929, 3327, 3840, 4400, 4953, 5727, 6500, 7335, 8388, 9521, 10686, 12198, 13775

Offset

-1,3

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

a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 30 2018

Expansion of A - q/A, where A = q^(1/2)*(eta(q^3)*eta(q^7)/(eta(q)* eta(q^21))), in powers of q. - G. C. Greubel, Jun 19 2018

Example

T42a = 1/q + 3*q^3 + 3*q^5 + 3*q^7 + 6*q^9 + 7*q^11 + 6*q^13 + 12*q^15 + ...

Mathematica

CoefficientList[Series[(QPochhammer[x^3]^2 * QPochhammer[x^7]^2 - x*QPochhammer[x]^2 * QPochhammer[x^21]^2) / (QPochhammer[x] * QPochhammer[x^3] * QPochhammer[x^7] * QPochhammer[x^21]), {x, 0, 100}], x] (* Vaclav Kotesovec, May 30 2018 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^7]/( eta[q]*eta[q^21])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 19 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^7)/(eta(q)* eta(q^21))); Vec(A - q/A) \\ G. C. Greubel, Jun 19 2018

Crossrefs

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

Sequence in context: A219299 A219595 A219173 * A025497 A031502 A153004

Adjacent sequences: A058672 A058673 A058674 * A058676 A058677 A058678

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Vaclav Kotesovec, May 30 2018

Status

approved