A028524 Character of extremal vertex operator algebra of rank 15.

1, 0, 255, 3640, 27525, 154056, 713850, 2878920, 10432650, 34739200, 107930865, 316293000, 881570320, 2352362160, 6040988775, 14993606776, 36092638500, 84513447480, 192980579410, 430636071000, 940847483976, 2015771306800, 4241235245220, 8774382020520

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..23.

G. Hoehn (gerald(AT)math.ksu.edu), Selbstduale Vertexoperatorsuperalgebren und das Babymonster, Doctoral Dissertation, Univ. Bonn, Jul 15 1995 (pdf, ps).

Formula

G.f.: q^(5/4) * (b(q)^30 - 30*b(q)^6) where b(q) = q^(-1/24) * Product_{k>=0} (1+q^(2*k+1)). - Sean A. Irvine, Feb 04 2020

a(n) ~ 5^(1/4) * exp(Pi*sqrt(5*n)) / (2^(3/2) * n^(3/4)). - Vaclav Kotesovec, Feb 05 2020

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 + x^(2*k + 1))^30, {k, 0, nmax}] - 30*x*Product[(1 + x^(2*k + 1))^6, {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 05 2020 *)

Crossrefs

Cf. A007245, A097340, A028523, A028525, A028511, A000521.

Sequence in context: A160908 A038995 A068024 * A075940 A075945 A075941

Adjacent sequences: A028521 A028522 A028523 * A028525 A028526 A028527

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Feb 04 2020

Status

approved