A132041 Expansion of (eta(q) * eta(q^2) / (eta(q^5) * eta(q^10)))^2 in powers of q.

1, -2, -3, 6, 2, 2, -5, -16, 12, 2, 17, -10, -48, 56, 10, 24, -35, -126, 106, 14, 94, -70, -284, 296, 60, 152, -175, -620, 536, 80, 398, -320, -1243, 1218, 216, 652, -680, -2422, 2122, 328, 1435, -1190, -4470, 4240, 734, 2312, -2285, -8120, 7130, 1112, 4549, -3850, -14178, 13132, 2210

Offset

-1,2

Comments

A058099(n) = a(n) unless n=0.

McKay-Thompson series of class 10C for Monster with a(0)=-2.

Links

Seiichi Manyama, Table of n, a(n) for n = -1..10000

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

Euler transform of period 10 sequence [ -2, -4, -2, -4, 0, -4, -2, -4, -2, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = 25 / f(t) where q = exp(2 Pi i t).

G.f.: (Product_{k>0} (1-x^k)* (1-x^(2k))/( (1-x^(5k))* (1-x^(10k))))^2.

Example

G.f. = 1/q - 2 - 3*q + 6*q^2 + 2*q^3 + 2*q^4 - 5*q^5 - 16*q^6 + 12*q^7 + ...

Mathematica

a[ n_] := SeriesCoefficient[ 1/q (QPochhammer[ q] QPochhammer[ q^2] / (QPochhammer[ q^5] QPochhammer[ q^10]))^2, {q, 0, n}]; (* Michael Somos, Aug 26 2015 *)

Prog

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x  + A) * eta(x^2 + A) / (eta(x^5 + A) * eta(x^10 + A)))^2, n))};

Crossrefs

Sequence in context: A002171 A138515 A107410 * A225820 A153634 A224910

Adjacent sequences: A132038 A132039 A132040 * A132042 A132043 A132044

Keyword

sign

Author

Michael Somos, Aug 07 2007

Status

approved