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A210796 Triangle of coefficients of polynomials v(n,x) jointly generated with A210795; see the Formula section.

%I A210796 #5 Mar 30 2012 18:58:17
%S A210796 1,1,2,3,3,3,3,7,6,5,5,10,16,12,8,5,16,26,34,23,13,7,21,47,64,70,43,
%T A210796 21,7,29,68,123,147,140,79,34,9,36,104,200,304,324,274,143,55,9,46,
%U A210796 140,324,538,714,690,527,256,89,11,55,195,480,932,1366,1616,1431
%N A210796 Triangle of coefficients of polynomials v(n,x) jointly generated with A210795; see the Formula section.
%C A210796 Row n starts with A109613(n) and ends with F(n+1), where F=A000045 (Fibonacci numbers).
%C A210796 Column 2: A114113
%C A210796 For a discussion and guide to related arrays, see A208510.
%F A210796 u(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F A210796 v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x),
%F A210796 where u(1,x)=1, v(1,x)=1.
%e A210796 First five rows:
%e A210796 1
%e A210796 1...2
%e A210796 3...3....3
%e A210796 3...7....6....5
%e A210796 5...10...16...12...8
%e A210796 First three polynomials v(n,x): 1, 1 + 2x, 3 + 3x + 3x^2
%t A210796 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210796 u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
%t A210796 d[x_] := h + x; e[x_] := p + x;
%t A210796 v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
%t A210796 j = 0; c = 1; h = 2; p = -1; f = 0;
%t A210796 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210796 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210796 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210796 TableForm[cu]
%t A210796 Flatten[%]   (* A210795 *)
%t A210796 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210796 TableForm[cv]
%t A210796 Flatten[%]   (* A210796 *)
%Y A210796 Cf. A210795, A208510.
%K A210796 nonn,tabl
%O A210796 1,3
%A A210796 _Clark Kimberling_, Mar 26 2012