A206299 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..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of (1/q) * chi(q) * chi(q^12)^3 / (chi(q^3)^3 * chi(q^4)) in powers of q where chi() is a Ramanujan theta function.

Expansion of c(q^2)*c(q^4)/(c(q)*c(q^8)) in powers of q where c() is a cubic AGM theta function.

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

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

Expansion of eta(q)*eta(q^6)^3*eta(q^8)*eta(q^12)^3/(eta(q^2)*eta(q^3)^3* eta(q^4)*eta(q^24)^3) in powers of q. - G. C. Greubel, Jun 20 2018

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]*QP[q^6]^3*QP[q^8]*(QP[q^12]^3/(QP[q^2]* QP[q^3]^3*QP[q^4]*QP[q^24]^3)) + O[q]^60; CoefficientList[s, q] (* Jean-François Alcover, Nov 16 2015, adapted from PARI *)

Prog

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^6 + A)^3 * eta(x^8 + A) * eta(x^12 + A)^3 / (eta(x^2 + A) * eta(x^3 + A)^3 * eta(x^4 +A ) * eta(x^24 + A)^3), n))}

Crossrefs

Cf. A058573, A206298, A184990.

Sequence in context: A144025 A058573 A184990 * A276053 A117268 A361076

Adjacent sequences: A206296 A206297 A206298 * A206300 A206301 A206302

Keyword

sign

Author

Michael Somos, Feb 05 2012

Status

approved