A028512 Character of extremal vertex operator algebra of rank 16.

1, 496, 69752, 2115008, 34670620, 394460000, 3499148224, 25817318016, 165011628166, 939112182480, 4853601292512, 23116070653888, 102602164703800, 428200065370144, 1692346392263680, 6371305129660032

Offset

0,2

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 (terms 0..1000 from Seiichi Manyama)

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

Formula

Square of A007245.

(q*j(q))^(2/3) where j(q) is the elliptic modular invariant. - Seiichi Manyama, Jul 15 2017

a(n) ~ exp(4*Pi*sqrt(2*n/3)) / (6^(1/4)*n^(3/4)). - Vaclav Kotesovec, Jul 15 2017

Mathematica

CoefficientList[Series[(QPochhammer[x, x^2]^8 + 256*x/QPochhammer[x, x^2]^16)^2, {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 15 2017 *)
CoefficientList[Series[(65536 + x*QPochhammer[-1, x]^24)^2 / (2*QPochhammer[-1, x])^16, {x, 0, 20}], x] (* Vaclav Kotesovec, Sep 23 2017 *)

Crossrefs

Cf. A000521 (j(q)).

(q*j(q))^(k/24): A289397 (k=-1), A106205 (k=1), A289297 (k=2), A289298 (k=3), A289299 (k=4), A289300 (k=5), A289301 (k=6), A289302 (k=7), A007245 (k=8), A289303 (k=9), A289304 (k=10), A289305 (k=11), A161361 (k=12), this sequence (k=16), A028513 (k=32), A028514 (k=40), A028515 (k=48).

Sequence in context: A249322 A110847 A160472 * A337952 A088845 A013685

Adjacent sequences: A028509 A028510 A028511 * A028513 A028514 A028515

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved