A028546 Character of extremal vertex operator algebra of rank 41/2.

1, 0, 0, 5986, 70930, 684823, 4554895, 25784285, 124544429, 541577200, 2142536303, 7874214410, 27111618590, 88375985276, 274361915435, 816223635550, 2336827590285, 6464455999320, 17332496822417, 45169505417075, 114679191847782, 284240995638700, 689000215557685

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..22.

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 = 41/2. - 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 = 41/2. - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 30; With[{r=41/2}, 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}] + (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: A274362 A233871 A182295 * A390829 A055108 A046903

Adjacent sequences: A028543 A028544 A028545 * A028547 A028548 A028549

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved