A028537 Character of extremal vertex operator algebra of rank 16.

1, 0, 0, 7936, 2296, 412672, 65536, 8777216, 1085468, 117516288, 12320768, 1168488704, 109365184, 9394478080, 806748160, 64249840128, 5156716678, 386395015168, 29347020800, 2091202273536, 151675552480, 10358666717184, 722376130560, 47567642539520

Offset

0,4

References

G. Höhn, Selbstduale Vertexoperatorsuperalgebren und das Babymonster, Bonner Mathematische Schriften, Vol. 286 (1996), 1-85.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

G. Höhn (gerald(AT)math.ksu.edu), Selbstduale Vertexoperatorsuperalgebren und das Babymonster, Doctoral Dissertation, Univ. Bonn, Jul 15 1995 (pdf, ps).

Formula

G.f.: x^(2*r/24) * (B(x)^(2*r) - 2*r*B(x)^(2*r-24) - r*(47-2*r)*B(x)^(2*r-48)) where B(x) = x^(-1/24) * Product_{k>=0} (1+x^(2*k+1)) = x^(-1/24) * A000700 and r = 16. - Sean A. Irvine, Feb 29 2020

a(n) ~ (16 - 15*(-1)^n) * exp(4*Pi*sqrt(n/3)) / (2^(9/2) * 3^(1/4) * n^(3/4)) * (1 - (3^(3/2)/(32*Pi) + 8*Pi/3^(3/2))/sqrt(n)). - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 30; With[{r=16}, CoefficientList[Series[Product[(1 + x^(2*k + 1))^(2*r), {k, 0, nmax}] - 2*r*x*Product[(1 + x^(2*k + 1))^(2*r - 24), {k, 0, nmax}] + (2*r-47)*r*x^2*Product[(1 + x^(2*k + 1))^(2*r - 48), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 16 2025 *)

Crossrefs

Cf. A000700.

Sequence in context: A031767 A250629 A185466 * A302901 A179708 A162010

Adjacent sequences: A028534 A028535 A028536 * A028538 A028539 A028540

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved