A028543 Character of extremal vertex operator algebra of rank 19.

1, 0, 0, 6726, 51490, 522538, 2819011, 15598126, 66776089, 278409356, 1012789015, 3553473100, 11459870045, 35680739958, 104848228086, 298518570528, 814386983257, 2161013972842, 5546772124012, 13896849891232, 33892153400144, 80925183641844, 188938349276850

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 = 19. - 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 = 19. - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 30; With[{r=19}, 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: A345838 A237041 A031580 * A145320 A035905 A099778

Adjacent sequences: A028540 A028541 A028542 * A028544 A028545 A028546

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved