A028530 Character of extremal vertex operator algebra of rank 21/2.

1, 0, 273, 1225, 6699, 24276, 83727, 249273, 706251, 1849449, 4634679, 11043102, 25418694, 56429226, 121771023, 255577105, 524104602, 1051048467, 2067033325, 3990581847, 7577271786, 14163504079, 26096985684, 47437304901, 85152306694, 151047652140, 264977541885

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 = 21/2. - 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 = 21/2. - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 30; With[{r=21/2}, 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: A306812 A157374 A043467 * A200836 A276980 A350303

Adjacent sequences: A028527 A028528 A028529 * A028531 A028532 A028533

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved