A028511 q-expansion of character of vertex-operator superalgebra of rank 23.5 on which Baby Monster group acts.

1, 0, 0, 4371, 96256, 1143745, 9646891, 64680601, 366845011, 1829005611, 8223700027, 33950840617, 130416170627, 470887671187, 1610882889457, 5254605009307, 16428803075153, 49446546607298, 143782211788218

Offset

0,4

References

T. Gannon, Moonshine Beyond the Monster, Cambridge, 2006; see p. 423.

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

Links

Table of n, a(n) for n=0..18.

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

Formula

Let X=sqrt( Sum (q^(m^2/2), m=-inf..inf) / q^(1/24) Product( 1-q^n, n=1..inf ) ). Then series is X^47 - 47*X^23.

a(n) ~ 47^(1/4) * exp(Pi*sqrt(47*n/6)) / (2^(7/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Feb 05 2020

Example

G.f. = 1 + 4371*x^3 + 96256*x^4 + 1143745*x^5 + 9646891*x^6 + 64680601*x^7 + ...
G.f. = q^(-47/48) * (1 + 4371 * q^(3/2) + 96256 * q^2 + 1143745 * q^(5/2) + ...).

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 + x^(2*k + 1))^47, {k, 0, nmax}] - 47*x*Product[(1 + x^(2*k + 1))^23, {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 05 2020 *)

Prog

(PARI) {a(n) = local(A); if( n<0, 0, A = prod( i=1, (1+n)\2, 1 + x^(2*i-1), 1 + x * O(x^n)); polcoeff( A^47 - 47 * x * A^23, n))}; /* Michael Somos, Jul 01 2004 */

Crossrefs

Cf. A007245 (rank 8), A097340 (rank 12), A028523 (rank 14), A028524 (rank 15), A028525 (rank 15.5), A000521 (rank 24).

Sequence in context: A190135 A207047 A001378 * A101558 A163583 A203403

Adjacent sequences: A028508 A028509 A028510 * A028512 A028513 A028514

Keyword

nonn

Author

N. J. A. Sloane

Status

approved