A028533 Character of extremal vertex operator algebra of rank 15/2.

1, 0, 275, 2325, 13250, 60630, 235500, 811950, 2558550, 7502125, 20713510, 54345125, 136483650, 329961125, 771284875, 1749490890, 3862641750, 8322360225, 17536187350, 36204137500, 73353404405, 146061623625, 286183499150, 552361219750, 1051231017125

Offset

0,3

References

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

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

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 = 25/2. - Sean A. Irvine, Feb 29 2020

a(n) ~ sqrt(5) * exp(5*Pi*sqrt(n/6)) / (2^(7/4) * 3^(1/4) * n^(3/4)) * (1 - (9/(20*Pi) + 125*Pi/48)/sqrt(6*n)). - Vaclav Kotesovec, May 16 2025

Mathematica

nmax = 40; CoefficientList[Series[Product[(1 + x^(2*k + 1))^25, {k, 0, nmax}] - 25*x*Product[(1 + x^(2*k + 1)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 16 2025 *)

Crossrefs

Cf. A000700.

Sequence in context: A250736 A063368 A028531 * A257123 A130292 A133536

Adjacent sequences: A028530 A028531 A028532 * A028534 A028535 A028536

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 29 2020

Status

approved