A028535 Character of extremal vertex operator algebra of rank 27/2.

1, 0, 270, 2871, 18171, 89991, 375741, 1380456, 4602852, 14210922, 41167332, 112987953, 296065548, 745155153, 1809970083, 4259274975, 9741874320, 21715729830, 47285705676, 100777629492, 210581716518, 432065232288, 871606268064, 1730764182321, 3386501211393

Offset

0,3

References

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

Links

Table of n, a(n) for n=0..24.

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)) where B(x) = x^(-1/24) * Product_{k>=0} (1+x^(2*k+1)) = x^(-1/24) * A000700 and r = 27/2. - 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 = 27/2. - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 30; With[{r=27/2}, 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

Cf. A000700.

Sequence in context: A029770 A028529 A109025 * A108094 A162007 A289136

Adjacent sequences: A028532 A028533 A028534 * A028536 A028537 A028538

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved