A028529 Character of extremal vertex operator algebra of rank 10.

1, 0, 270, 960, 5725, 18304, 64150, 178240, 502630, 1257600, 3108856, 7163200, 16219955, 35048320, 74331550, 152459008, 307296950, 603802880, 1167637650, 2212721600, 4133756892, 7594956800, 13776792930, 24641263360, 43571462525, 76116608128, 131607454150

Offset

0,3

References

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

Links

Table of n, a(n) for n=0..26.

G. Hoehn (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)) where B(x) = x^(-1/24) * Product_{k>=0} (1+x^(2*k+1)) = x^(-1/24) * A000700 and r = 10. - Sean A. Irvine, Feb 29 2020

a(n) ~ r^(1/4)*exp(Pi*sqrt(r*n/3)) / (2^(3/2) * 3^(1/4) * n^(3/4)) * (1 - (3^(3/2)/(8*Pi*sqrt(r)) + Pi*r^(3/2)/(8*3^(3/2)))/sqrt(n)), where r = 10. - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 30; With[{r=10}, 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}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 16 2025 *)

Crossrefs

Sequence in context: A278130 A206088 A029770 * A109025 A028535 A108094

Adjacent sequences: A028526 A028527 A028528 * A028530 A028531 A028532

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved