A028528 - OEIS

A028528

Character of extremal vertex operator algebra of rank 19/2.

1, 0, 266, 703, 4997, 13091, 49989, 122474, 360753, 828400, 2087644, 4524014, 10306531, 21258834, 45004122, 88974283, 178190303, 339675540, 650850434, 1202008572, 2221390339, 3990403142, 7153670354, 12539899946, 21903187213, 37568267009, 64150343834

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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..26.

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 = 19/2. - 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 = 19/2. - Vaclav Kotesovec, May 16 2025

MATHEMATICA

nmax = 30; With[{r=19/2}, 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

Sequence in context: A061662 A348657 A321224 * A260134 A242320 A225935

Adjacent sequences: A028525 A028526 A028527 * A028529 A028530 A028531

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sean A. Irvine, Feb 29 2020

STATUS

approved