A184990 McKay-Thompson series of class 24C for the Monster group with a(0) = 1.

1, 1, 0, 2, -1, -2, 4, -2, -2, 6, -4, -4, 10, -6, -8, 16, -9, -10, 24, -14, -16, 36, -20, -24, 53, -30, -32, 76, -43, -48, 108, -60, -68, 150, -84, -92, 206, -114, -128, 280, -155, -172, 376, -208, -228, 504, -276, -304, 668, -366, -400, 878, -480, -524, 1148

Offset

-1,4

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = -1..5000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of (1/q) * psi(q) * phi(-q^4) / (psi(-q^3) * psi(-q^6)) in powers of q where phi(), psi() are Ramanujan theta functions.

Expansion of eta(q^2)^2 * eta(q^4)^2 / (eta(q) * eta(q^3) * eta(q^8)* eta(q^24)) in powers of q.

Euler transform of period 24 sequence [ 1, -1, 2, -3, 1, 0, 1, -2, 2, -1, 1, -2, 1, -1, 2, -2, 1, 0, 1, -3, 2, -1, 1, 0, ...].

a(n) = A058573(n) unless n = 0.

Example

1/q + 1 + 2*q^2 - q^3 - 2*q^4 + 4*q^5 - 2*q^6 - 2*q^7 + 6*q^8 - 4*q^9 + ...

Mathematica

QP = QPochhammer; s=QP[q^2]^2*(QP[q^4]^2/(QP[q]*QP[q^3]*QP[q^8]*QP[q^24]))+ O[q]^60; CoefficientList[s, q] (* Jean-François Alcover, Nov 14 2015, adapted from PARI *)

Prog

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^4 + A)^2 / (eta(x + A) * eta(x^3 + A) * eta(x^8 + A)* eta(x^24 + A)), n))}

Crossrefs

Cf. A058573.

Sequence in context: A152251 A144025 A058573 * A206299 A276053 A117268

Adjacent sequences: A184987 A184988 A184989 * A184991 A184992 A184993

Keyword

sign

Author

Michael Somos, Feb 05 2012

Status

approved