[seqfan] Re: Another variant of the Catalan triangle.

[Ed Jeffery]

Peter Luschny and Richard Mathar,

Thank you both for the links.

A053121 [1] is clearly the closest version of that triangle. I noticed
before that for the Chebyshev S-polynomials [1], defined by

(1)  S_0(x) = 1, S_1(x) = x, S_r(x) = x*S_{r-1}(x) - S_{r-2}(x), r>1,

holds the identity

x^n = Sum_{k=0,...,n } A053121(n,k),

which is quite useful. (In fact, I often define x to be a square matrix
rather than a scalar in (1).)

Peter, your blog is excellent and very interesting. Thanks again.

LEJ

References:

[1] Sequence A053121, https://oeis.org/A053121
[2] W. Lang, Chebyshev S-polynomials (draft),
http://www-itp.particle.uni-karlsruhe.de/~wl/EISpub/A049310appl.pdf