A058578 McKay-Thompson series of class 24H for Monster.

1, 2, 5, 8, 14, 22, 34, 52, 75, 108, 152, 212, 293, 398, 539, 720, 956, 1260, 1646, 2140, 2761, 3548, 4532, 5760, 7292, 9186, 11532, 14416, 17958, 22292, 27576, 34012, 41815, 51264, 62672, 76416, 92941, 112756, 136481, 164816, 198602, 238810

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Given g.f. A(x), then B(x)=A(x^2)^2/x^2 satisfies 0=f(B(x), B(x^2)) where f(u, v)= -uv(1+u^2v^2) +7uv(u+v)(1+uv) +9uv(u^2+v^2). - Michael Somos, May 16 2004

Expansion of q^(1/2)(eta(q^3)eta(q^4)/(eta(q)eta(q^12)))^2 in powers of q. - Michael Somos, May 16 2004

Euler transform of period 12 sequence [2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, ...]. - Michael Somos, May 16 2004

a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(5/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 10 2015

Example

T24H = 1/q + 2*q + 5*q^3 + 8*q^5 + 14*q^7 + 22*q^9 + 34*q^11 + 52*q^13 + ...

Mathematica

nmax = 50; CoefficientList[Series[Product[((1-x^(3*k)) * (1-x^(4*k)) / ((1-x^k) * (1-x^(12*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 10 2015 *)

Prog

(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff((eta(x^3+A)*eta(x^4+A)/eta(x+A)/eta(x^12+A))^2, n)) /* Michael Somos, May 16 2004 */

Crossrefs

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A182377 A327380 A330378 * A261526 A295392 A023674

Adjacent sequences: A058575 A058576 A058577 * A058579 A058580 A058581

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Status

approved