A282877 McKay-Thompson series of class 7A for the Monster group with a(0) = 9.

1, 9, 51, 204, 681, 1956, 5135, 12360, 28119, 60572, 125682, 251040, 487426, 920568, 1699611, 3070508, 5445510, 9490116, 16283793, 27537708, 45959775, 75760640, 123471327, 199081632, 317814988, 502608456, 787889775, 1224834672, 1889206080, 2892264900

Offset

-1,2

References

B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 176 Entry 32(iii).

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000

Formula

Expansion of (eta(q)/eta(q^7))^4 + 13 + 49*(eta(q^7)/eta(q))^4 in powers of q.

G.f. is a period 1 Fourier series which satisfies f(-1 / (9 t)) = f(t) where q = exp(2 Pi i t).

Convolution cube of A058576.

a(n) ~ exp(4*Pi*sqrt(n/7)) / (sqrt(2)*7^(1/4)*n^(3/4)). - Vaclav Kotesovec, Feb 26 2017

Example

G.f. = 1/q + 9 + 51*q + 204*q^2 + 681*q^3 + 1956*q^4 + 5135*q^5 + 12360*q^6 + ...

Mathematica

a[ n_] := With[ {A = q (QPochhammer[ q^7] / QPochhammer[ q])^4}, SeriesCoefficient[ 1/A + 13 + 49 A, {q, 0, n}]];

Prog

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x^7 + A) / eta(x + A))^4; polcoeff( 1/A + 13*x + 49*x^2 * A, n))};

Crossrefs

Cf. A007264, A030183, A045489, A058576.

Sequence in context: A034816 A140381 A330805 * A055900 A054549 A005746

Adjacent sequences: A282874 A282875 A282876 * A282878 A282879 A282880

Keyword

nonn

Author

Michael Somos, Feb 23 2017

Status

approved