A028512 - OEIS

%I #23 Sep 23 2017 17:56:51

%S 1,496,69752,2115008,34670620,394460000,3499148224,25817318016,

%T 165011628166,939112182480,4853601292512,23116070653888,

%U 102602164703800,428200065370144,1692346392263680,6371305129660032

%N Character of extremal vertex operator algebra of rank 16.

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

%H Vaclav Kotesovec, <a href="/A028512/b028512.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Seiichi Manyama)

%H G. Hoehn (gerald(AT)math.ksu.edu), Selbstduale Vertexoperatorsuperalgebren und das Babymonster, Doctoral Dissertation, Univ. Bonn, Jul 15 1995 (<a href="http://www.math.ksu.edu/~gerald/papers/dr.pdf">pdf</a>, <a href="http://www.math.ksu.edu/~gerald/papers/dr.ps.gz">ps</a>).

%F Square of A007245.

%F (q*j(q))^(2/3) where j(q) is the elliptic modular invariant. - _Seiichi Manyama_, Jul 15 2017

%F a(n) ~ exp(4*Pi*sqrt(2*n/3)) / (6^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Jul 15 2017

%t CoefficientList[Series[(QPochhammer[x, x^2]^8 + 256*x/QPochhammer[x, x^2]^16)^2, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jul 15 2017 *)

%t CoefficientList[Series[(65536 + x*QPochhammer[-1, x]^24)^2 / (2*QPochhammer[-1, x])^16, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Sep 23 2017 *)

%Y Cf. A000521 (j(q)).

%Y (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).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_