A258094 McKay-Thompson series of class 6E for the Monster group with a(0) = 7.

1, 7, 6, 4, -3, -12, -8, 12, 30, 20, -30, -72, -46, 60, 156, 96, -117, -300, -188, 228, 552, 344, -420, -1008, -603, 732, 1770, 1048, -1245, -2976, -1776, 2088, 4908, 2900, -3420, -7992, -4658, 5460, 12756, 7408, -8583, -19944, -11564, 13344, 30756, 17744

Offset

-1,2

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).

Links

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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of q^(-1) * a(q) * psi(q) / psi(q^3)^3 in powers of q where psi() is a Ramanujan theta function and a() is a cubic AGM theta function.

Expansion of 12 + eta(q)^5 * eta(q^3) / (eta(q^2) * eta(q^6)^5) in powers of q.

Convolution of A004016 and A258093.

Example

G.f. = 1/q + 7 + 6*q + 4*q^2 - 3*q^3 - 12*q^4 - 8*q^5 + 12*q^6 + 30*q^7 + ...

Mathematica

QP = QPochhammer; s = 4*q + (QP[q^2]*(QP[q^3]^3/(QP[q]*QP[q^6]^3)))^3 + O[q]^50; CoefficientList[s, q] (* Jean-François Alcover, Nov 15 2015, adapted from PARI *)

Prog

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( 4*x + (eta(x^2 + A) * eta(x^3 + A)^3 / (eta(x + A) * eta(x^6 + A)^3))^3, n))};

Crossrefs

Cf. A004016, A258093.

Essentially the same as A128633, A128632, A105559, A045488 and A007258.

Sequence in context: A242967 A228628 A131266 * A258008 A021089 A154194

Adjacent sequences: A258091 A258092 A258093 * A258095 A258096 A258097

Keyword

sign

Author

Michael Somos, May 19 2015

Status

approved