A028539 Character of extremal vertex operator algebra of rank 17.

1, 0, 0, 7582, 19907, 413678, 956573, 9163204, 20235644, 128121010, 274454086, 1331787072, 2786077946, 11198909732, 22949142928, 80096132094, 161086799989, 503513373888, 995154766305, 2846600748484, 5534753633023, 14717879636288, 28177487199544, 70484779859958

Offset

0,4

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) - r*(47-2*r)*B(x)^(2*r-48)) where B(x) = x^(-1/24) * Product_{k>=0} (1+x^(2*k+1)) = x^(-1/24) * A000700 and r = 17. - 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 = 17. - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 30; With[{r=17}, 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}]   + (2*r-47)*r*x^2*Product[(1 + x^(2*k + 1))^(2*r - 48), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 16 2025 *)

Crossrefs

Cf. A000700.

Sequence in context: A257204 A204358 A232547 * A234204 A190077 A355119

Adjacent sequences: A028536 A028537 A028538 * A028540 A028541 A028542

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved