A058678 McKay-Thompson series of class 42d for Monster.

1, 1, 2, 2, 4, 5, 7, 8, 12, 14, 20, 23, 31, 37, 47, 56, 71, 84, 104, 122, 151, 178, 215, 252, 303, 355, 423, 492, 582, 676, 795, 920, 1076, 1242, 1445, 1662, 1926, 2210, 2549, 2916, 3353, 3827, 4386, 4992, 5703, 6478, 7379, 8362, 9499, 10742, 12174, 13738, 15533, 17496, 19736, 22190, 24979

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

Expansion of q^(1/2)*(eta(q^3)*eta(q^7)/(eta(q)*eta(q^21))) in powers of q. - G. C. Greubel, Jun 26 2018

a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

Example

T42d = 1/q + q + 2*q^3 + 2*q^5 + 4*q^7 + 5*q^9 + 7*q^11 + 8*q^13 + 12*q^15 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q^3]*eta[q^7]/(eta[q]*eta[q^21])), {q, 0, 60}], q]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jun 26 2018 *)

Prog

(PARI) q='q+O('q^60); Vec(eta(q^3)*eta(q^7)/(eta(q)*eta(q^21))) \\ G. C. Greubel, Jun 26 2018

Crossrefs

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

Sequence in context: A029007 A338202 A348552 * A241410 A324753 A374020

Adjacent sequences: A058675 A058676 A058677 * A058679 A058680 A058681

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 26 2018

Status

approved