A058746 McKay-Thompson series of class 70a for Monster.

1, 1, 0, 2, 1, 2, 1, 2, 3, 4, 5, 5, 5, 7, 8, 11, 10, 13, 14, 16, 19, 22, 23, 28, 32, 37, 38, 45, 51, 58, 65, 73, 78, 91, 98, 114, 123, 136, 153, 170, 187, 206, 226, 255, 276, 312, 334, 369, 406, 448, 492, 538, 586, 646, 701, 773, 837, 917, 997, 1093, 1188, 1291, 1397, 1532, 1657, 1808

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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of sqrt(2 + T35A) in powers of q, where T35A = A058640. - 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, Jul 02 2018

Example

T70a = 1/q + q + 2*q^5 + q^7 + 2*q^9 + q^11 + 2*q^13 + 3*q^15 + 4*q^17 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 80; B:= eta[q^5]*eta[q^7]/( eta[q]*eta[q^35]); a:= CoefficientList[Series[(q (1 + B - 1/B + O[q]^nmax))^(1/2), {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^5)*eta(q^7)/(q*eta(q)*eta(q^35)); Vec(sqrt(q*(B + 1 - 1/B))) \\ G. C. Greubel, Jul 01 2018

Crossrefs

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

Sequence in context: A261273 A097454 A139803 * A080916 A071622 A182063

Adjacent sequences: A058743 A058744 A058745 * A058747 A058748 A058749

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 30 2018

Status

approved