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A163762 Triangle of coefficients of polynomials H(n,x)=(U^n+L^n)/2+(U^n-L^n)/(2d), where U=x+d, L=x-d, d=(x+4)^(1/2).

%I A163762 #2 Mar 30 2012 18:57:11
%S A163762 1,1,1,1,3,4,1,6,13,4,1,10,29,24,16,1,15,55,81,88,16,1,21,95,207,300,
%T A163762 144,64,1,28,154,448,813,684,496,64,1,36,238,868,1913,2352,2272,768,
%U A163762 256,1,45,354,1554,4077,6625,7984,4704,2560,256,1,55,510,2622,8061,16283
%N A163762 Triangle of coefficients of polynomials H(n,x)=(U^n+L^n)/2+(U^n-L^n)/(2d), where U=x+d, L=x-d, d=(x+4)^(1/2).
%C A163762 H(n,x)=P(n,x)+Q(n,x), where P and Q are given by A162516, A162517.
%C A163762 H(n,0)=4^Floor(n/2) for n=0,1,2,...
%C A163762 H(n,1)=A063727(n); row sums
%C A163762 (Column 2)=A000217 (triangular numbers)
%F A163762 H(n,x)=2*x*H(n-1,x)-(x^2-x-4)*H(n-2,x), where H(0,x)=1, H(1,x)=x+1.
%F A163762 H(n,x)=(1+1/d)*U^n+(1-1/d)*L^n, where U=x+d, L=x-d, d=(x+4)^(1/2).
%e A163762 First six rows:
%e A163762 1
%e A163762 1...1
%e A163762 1...3...4
%e A163762 1...6..13...4
%e A163762 1..10..29..24..16
%e A163762 1..15..55..81..88..16
%e A163762 Row 6 represents x^5+15*x^4+55*x^3+81*x^2+88*x+16.
%Y A163762 A000217, A063727, A162516, A162517.
%K A163762 nonn,tabl
%O A163762 1,5
%A A163762 _Clark Kimberling_, Aug 04 2009