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A210798 Triangle of coefficients of polynomials v(n,x) jointly generated with A210797; see the Formula section.

%I A210798 #5 Mar 30 2012 18:58:17
%S A210798 1,2,2,1,3,3,2,5,7,5,1,6,12,13,8,2,8,20,29,25,13,1,9,27,51,62,46,21,2,
%T A210798 11,39,84,125,129,84,34,1,12,48,126,224,284,258,151,55,2,14,64,182,
%U A210798 374,562,622,505,269,89,1,15,75,250,580,1008,1328,1315,969,475
%N A210798 Triangle of coefficients of polynomials v(n,x) jointly generated with A210797; see the Formula section.
%C A210798 Row n starts with A109613(n) and ends with F(n+1), where F=A000045 (Fibonacci numbers).
%C A210798 Column 2: A114113
%C A210798 For a discussion and guide to related arrays, see A208510.
%F A210798 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A210798 v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x)+1,
%F A210798 where u(1,x)=1, v(1,x)=1.
%e A210798 First five rows:
%e A210798 1
%e A210798 2...2
%e A210798 1...3...3
%e A210798 2...5...7....5
%e A210798 1...6...12...13...8
%e A210798 First three polynomials v(n,x): 1, 2 + 2x, 1 + 3x + 3x^2
%t A210798 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210798 u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
%t A210798 d[x_] := h + x; e[x_] := p + x;
%t A210798 v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
%t A210798 j = 0; c = 0; h = 2; p = -1; f = 1;
%t A210798 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210798 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210798 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210798 TableForm[cu]
%t A210798 Flatten[%]    (* A210797 *)
%t A210798 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210798 TableForm[cv]
%t A210798 Flatten[%]    (* A210798 *)
%t A210798 Table[u[n, x] /. x -> 1, {n, 1, z}]   (* A099232 *)
%t A210798 Table[v[n, x] /. x -> 1, {n, 1, z}]   (* A006130 *)
%t A210798 Table[u[n, x] /. x -> -1, {n, 1, z}]  (* A008346 *)
%t A210798 Table[v[n, x] /. x -> -1, {n, 1, z}]  (* A039834 *)
%Y A210798 Cf. A210797, A208510.
%K A210798 nonn,tabl
%O A210798 1,2
%A A210798 _Clark Kimberling_, Mar 26 2012