A028527 - OEIS

A028527

Character of extremal vertex operator algebra of rank 9.

1, 0, 261, 456, 4500, 8424, 40641, 77040, 269235, 506456, 1446723, 2681136, 6704277, 12202272, 27687267, 49457064, 104319477, 182912400, 364276801, 627412968, 1193103936, 2020392312, 3698191305, 6163298280, 10925899518, 17938040328, 30941176770, 50091366752

(list; graph; refs; listen; history; text; internal format)

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..27.

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 = 9. - 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 = 9. - Vaclav Kotesovec, May 16 2025

MATHEMATICA

nmax = 30; With[{r=9}, 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: A345814 A131062 A079506 * A014569 A063364 A264894

Adjacent sequences: A028524 A028525 A028526 * A028528 A028529 A028530

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sean A. Irvine, Feb 29 2020

STATUS

approved