A028532 Character of extremal vertex operator algebra of rank 23/2.

1, 0, 276, 1771, 9430, 39445, 142531, 460391, 1370156, 3810341, 10013717, 25082282, 60303447, 139869762, 314255118, 686285408, 1461010508, 3039221633, 6190257789, 12366731770, 24269856335, 46851441255, 89069526921, 166930973477, 308709141202, 563802228832

Offset

0,3

References

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

Links

Table of n, a(n) for n=0..25.

G. Hoehn (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 = 23/2. - 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 = 23/2. - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 30; With[{r=23/2}, 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, A007246.

Sequence in context: A343426 A015232 A128382 * A028522 A007246 A107080

Adjacent sequences: A028529 A028530 A028531 * A028533 A028534 A028535

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved