A028536 Character of extremal vertex operator algebra of rank 29/2.

1, 0, 261, 3393, 24157, 129688, 580609, 2270671, 8004754, 25996789, 78925762, 226351177, 618182705, 1618088408, 4079878514, 9950251364, 23552795295, 54265058448, 121990170516, 268139111685, 577310192290, 1219427979865, 2530473375487, 5165077677896

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..23.

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 = 29/2. - 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 = 29/2. - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 30; With[{r=29/2}, 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: A014569 A063364 A264894 * A238909 A263910 A345568

Adjacent sequences: A028533 A028534 A028535 * A028537 A028538 A028539

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved