OFFSET

0,2

COMMENTS

Row indices q begin with 1, column indices n begin with 0.

LINKS

S. Barbero, Dickson Polynomials, Chebyshev Polynomials, and Some Conjectures of Jeffery, Journal of Integer Sequences, 17 (2014), #14.3.8.

FORMULA

Conjecture. The n-th entry in row q is given by R_q(n) = 2^(2*n)*(sum_{j=1,...,n+1} (cos(j*Pi/(2*q+1)))^(2*n)), q >= 1, n >= 0.

Conjecture. G.f. for column n is of the form G_n(x) = H_n(x)/(1-x)^2, where H_n(x) is a polynomial in x, n >= 0.

EXAMPLE

Array begins as

1, 1, 1, 1, 1, 1, ...

2, 3, 7, 18, 47, 123, ...

3, 5, 13, 38, 117, 370, ...

4, 7, 19, 58, 187, 622, ...

5, 9, 25, 78, 257, 874, ...

6, 11, 31, 98, 327, 1126, ...

...

CROSSREFS

KEYWORD

nonn,tabl

AUTHOR

L. Edson Jeffery, Jan 23 2012

STATUS

approved