A058745 McKay-Thompson series of class 70B for Monster.

1, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, -1, 2, -2, 2, -1, 1, -2, 1, -1, 3, -2, 2, -4, 3, -2, 3, -4, 4, -4, 5, -6, 6, -7, 6, -4, 7, -8, 5, -8, 12, -11, 12, -14, 13, -12, 13, -14, 13, -14, 19, -21, 20, -24, 24, -22, 27, -27, 23, -30, 37, -34, 35, -40, 42, -40, 41

Offset

-1,13

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)*eta(q^10)*eta(q^14)*eta(q^35)/(eta(q^2)*eta(q^5) *eta(q^7)*eta(q^70)) in powers of q. - G. C. Greubel, Jun 30 2018

a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/35)) / (2 * 35^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 10 2018

Example

T70B = 1/q - q^2 + q^3 - q^8 + q^9 - q^10 + 2*q^11 - 2*q^12 + 2*q^13 - q^14 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; B:= eta[q]*eta[q^10]*eta[q^14]* eta[q^35]/(eta[q^2]*eta[q^5]*eta[q^7]*eta[q^70]); a:= CoefficientList[ Series[q*(1 + B), {q, 0, 105}], q]; Table[a[[n]], {n, 1, 100}] (* G. C. Greubel, Jun 30 2018 *)
nmax = 100; CoefficientList[x + Series[Product[(1 + x^(5*k))*(1 + x^(7*k))/((1 + x^k)*(1 + x^(35*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 10 2018 *)

Prog

(PARI) q='q+O('q^50); F = 1 + eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/(q* eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)); Vec(F) \\ G. C. Greubel, Jun 30 2018

Crossrefs

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

Sequence in context: A104637 A188795 A325444 * A275333 A108393 A327342

Adjacent sequences: A058742 A058743 A058744 * A058746 A058747 A058748

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 24 2014

Status

approved