A028531 Character of extremal vertex operator algebra of rank 11.

1, 0, 275, 1496, 7931, 31240, 109516, 341176, 988031, 2671856, 6849942, 16750912, 39391297, 89436072, 196915917, 421732432, 881208933, 1800324328, 3603551358, 7078487944, 13665932995, 25964272664, 48601312255, 89719964136, 163490906337, 294312308576

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..25.

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 = 11. - 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 = 11. - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 30; With[{r=11}, 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: A321487 A250736 A063368 * A028533 A257123 A130292

Adjacent sequences: A028528 A028529 A028530 * A028532 A028533 A028534

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved