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A058098 McKay-Thompson series of class 10B for the Monster group with a(0) = 0. 2
1, 0, 6, -8, 17, -32, 54, -80, 116, -192, 290, -408, 585, -832, 1192, -1648, 2237, -3072, 4156, -5576, 7414, -9824, 12964, -16896, 22002, -28544, 36794, -47184, 60185, -76736, 97388, -122864, 154615, -194048, 242904, -302800, 376271, -466720, 577176, -711840 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

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 (terms -1..997 from G. A. Edgar)

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

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of q^-1 * (chi(-q) * chi(-q^5))^4 + 4 in powers of q where chi() is a Ramanujan theta function.

Expansion of (eta(q) * eta(q^5) / (eta(q^2) * eta(q^10)))^4 + 4 in powers of q.

G.f.: (Product_{k>0} (1 + x^k) * (1 + x^(5*k)))^-4 + 4.

a(n) = A132040(n) unless n = 0. a(n) = -(-1)^n * A112158(n). - Michael Somos, Feb 02 2012

a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 08 2017

EXAMPLE

T10B = 1/q + 6*q - 8*q^2 + 17*q^3 - 32*q^4 + 54*q^5 - 80*q^6 + ...

MATHEMATICA

QP = QPochhammer; s = (QP[q]*(QP[q^5]/QP[q^2]/QP[q^10]))^4 + 4*q + O[q]^40; CoefficientList[s, q] (* Jean-Fran├žois Alcover, Nov 13 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^5 + A) / eta(x^2 + A) / eta(x^10 + A))^4 + 4 * x, n))} /* Michael Somos, Feb 02 2012 */

CROSSREFS

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

Cf. A112158, A132040.

Sequence in context: A025081 A162951 A032411 * A112158 A270046 A093479

Adjacent sequences:  A058095 A058096 A058097 * A058099 A058100 A058101

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved

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Last modified January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)