OFFSET
1,2
COMMENTS
Let Phi(n,q) be the n-th cyclotomic polynomial in q. The q-partial fraction decomposition of 1/Phi(n,q) is a representation of 1/Phi(n,q) as a finite sum of functions v(q)/(1-q^m)^t, such that m<=n and degree(v)<phi(m) (Euler's totient function A000010).
LINKS
Augustine O. Munagi, Computation of q-partial fractions, INTEGERS: Electronic Journal Of Combinatorial Number Theory, 7 (2007), #A25.
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
EXAMPLE
(i) a(3)=1 because 1/Phi(3,q)=(1-q)/(1-q^3);
(ii) a(6)=2 because 1/Phi(6,q)=(-1-q)/(1-q^3) + (2+2q)/(1-q^6).
CROSSREFS
KEYWORD
nonn
AUTHOR
Augustine O. Munagi, Jul 12 2007
STATUS
approved