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A028511 q-expansion of character of vertex-operator superalgebra of rank 23.5 on which Baby Monster group acts. 3
1, 0, 0, 4371, 96256, 1143745, 9646891, 64680601, 366845011, 1829005611, 8223700027, 33950840617, 130416170627, 470887671187, 1610882889457, 5254605009307, 16428803075153, 49446546607298, 143782211788218 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 26 22:13 EST 2023. Contains 359836 sequences. (Running on oeis4.)