|
%I #8 Aug 22 2015 02:14:51
%S 1,1,-1,1,-3,1,-7,1,1,-15,5,1,-31,17,-1,1,-63,49,-7,1,-127,129,-31,1,
%T 1,-255,321,-111,9,1,-511,769,-351,49,-1,1,-1023,1793,-1023,209,-11,1,
%U -2047,4097,-2815,769,-71,1,1,-4095,9217,-7423,2561,-351,13,1,-8191,20481,-18943,7937,-1471,97,-1
%N Irregular triangle read by rows: coefficients of polynomials V_n(x), highest degree terms first.
%H K. Dilcher, K. B. Stolarsky, <a href="http://dx.doi.org/10.1007/s11139-014-9620-5">Nonlinear recurrences related to Chebyshev polynomials</a>, The Ramanujan Journal, 2014, Online Oct. 2014, pp. 1-23.
%e Triangle begins:
%e 1,
%e 1, -1,
%e 1, -3,
%e 1, -7, 1,
%e 1, -15, 5,
%e 1, -31, 17, -1,
%e 1, -63, 49, -7,
%e 1, -127, 129, -31, 1,
%e 1, -255, 321, -111, 9,
%e 1, -511, 769, -351, 49, -1,
%e 1, -1023, 1793, -1023, 209, -11,
%e 1, -2047, 4097, -2815, 769, -71, 1,
%e 1, -4095, 9217, -7423, 2561, -351, 13,
%e 1, -8191, 20481, -18943, 7937, -1471, 97, -1,
%e ...
%o (PARI) tabf(nn) = {pp = 1; p = x; print(polcoeff(p, poldegree(p))); for (n=1, nn, np = 2*x*p-pp-x^(n+1); forstep (j=poldegree(np), 0, -1, if (c = polcoeff(np, j), print1(c, ", "));); pp = p; p = np; print(););} \\ _Michel Marcus_, Aug 22 2015
%Y A210197 is an essentially identical triangle.
%K sign,tabf
%O 1,5
%A _N. J. A. Sloane_, Jun 06 2015
|
