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).
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
KEYWORD
sign
AUTHOR
Michael Somos, Aug 07 2007
STATUS
approved