A058624 McKay-Thompson series of class 30c for Monster.

1, -1, -1, 1, -1, -1, 3, 0, -2, 4, -3, -2, 6, -3, -4, 8, -6, -6, 13, -8, -8, 18, -9, -11, 26, -13, -15, 32, -19, -20, 47, -26, -29, 60, -34, -36, 82, -42, -49, 104, -58, -61, 136, -72, -81, 174, -99, -104, 225, -122, -132, 284, -151, -166, 362, -194, -209, 448

Offset

0,7

Links

G. C. Greubel, 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

From Michael Somos, Mar 26 2004: (Start)

G.f. A(x)=y satisfies 0=f(A(x)^2/x,A(x^2)^2/x^2) where f(u,v) = u^3 + v^3 - 4uv(u+v) - 9uv - (uv)^2.

Euler transform of period 15 sequence [-1,-1,0,-1,-2,0,-1,-1,0,-2,-1,0,-1,-1,0,...].

Expansion of q^(1/2)*(eta(q)*eta(q^5))/(eta(q^3)*eta(q^15)) in powers of q. (End)

Example

T30c = 1/q - q - q^3 + q^5 - q^7 - q^9 + 3*q^11 - 2*q^15 + 4*q^17 - 3*q^19 - ...

Mathematica

QP = QPochhammer; s = (QP[q]*QP[q^5])/(QP[q^3]*QP[q^15]) + O[q]^60; CoefficientList[s, q] (* Jean-François Alcover, Nov 13 2015, adapted from PARI *)

Prog

(PARI) a(n)=local(X); if(n<0, 0, X=x+x*O(x^n); polcoeff((eta(X)*eta(X^5))/(eta(X^3)*eta(X^15)), n))

Crossrefs

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

Sequence in context: A178313 A190013 A171088 * A145856 A092154 A177344

Adjacent sequences: A058621 A058622 A058623 * A058625 A058626 A058627

Keyword

sign,changed

Author

N. J. A. Sloane, Nov 27 2000

Status

approved