OFFSET
0,5
COMMENTS
The denominator triangle is given by A181348.
Because exp(T) = F, T may be considered as generator of F.
This should be read as N x N matrix for N>=2: log(F_N) := -sum(((-1)^k)/k)*(F_N - Id_N)^k,N-1) with the lower triangular N x N matrix F_N := Matrix([seq([seq(A037027(n,m),n=0..N-1)],m=0..N-1)]) and the N x N identity matrix Id_N.
The log series terminates because of the lower triangular property, and the fact that all main diagonal elements are 1, which follows from
F = Riordan matrix (Fib(x),x*Fib(x)) with the o.g.f. Fib(x)=1/(1-x-x^2). For this notation of Riordan arrays see, e.g., the W.Lang link given in A006232, and there the paragraph "Summary on A- and Z-sequences for Riordan matrices", as well as the 1991 Shapiro et al. reference on the Riordan group given in A053121.
LINKS
FORMULA
a(n,m) = numerator((log F)(n,m)), with the Fibonacci lower triangular matrix F=A037027.
EXAMPLE
[0]; [1,0]; [1,2,0]; [-1,2,3,0]; [-1,-1,3,4,0];...
The rational triangle (with main diagonal elements 0) starts with the rows [0]; [1, 0]; [1, 2, 0]; [-1/2, 2, 3, 0]; [-1/3, -1, 3, 4, 0];...
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Oct 15 2010
STATUS
approved