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A209769 Triangle of coefficients of polynomials u(n,x) jointly generated with A209770; see the Formula section.

%I A209769 #6 Mar 30 2012 18:58:15
%S A209769 1,1,2,3,5,3,5,12,11,5,9,26,34,24,8,15,53,88,86,48,13,25,104,210,258,
%T A209769 200,93,21,41,198,470,695,680,440,175,34,67,369,1007,1737,2043,1671,
%U A209769 929,323,55,109,676,2085,4107,5625,5529,3895,1901,587,89,177
%N A209769 Triangle of coefficients of polynomials u(n,x) jointly generated with A209770; see the Formula section.
%C A209769 Column 1: A001595
%C A209769 Row n ends with F(n+1), where F=A000045 (Fibonacci numbers).
%C A209769 Row sums: 1,3,11,33,101,303,911,2733,... A081250
%C A209769 Alternating row sums: 1,-1,1,-1,1,-1,... A033999
%C A209769 For a discussion and guide to related arrays, see A208510.
%F A209769 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209769 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A209769 where u(1,x)=1, v(1,x)=1.
%e A209769 First five rows:
%e A209769 1
%e A209769 1...2
%e A209769 3...5....3
%e A209769 5...12...11...5
%e A209769 9...26...34...24...8
%e A209769 First three polynomials u(n,x): 1, 1 + 2x, 3 + 5x + 3x^2.
%t A209769 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209769 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209769 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A209769 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209769 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209769 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209769 TableForm[cu]
%t A209769 Flatten[%]    (* A209769 *)
%t A209769 Table[Expand[v[n, x]], {n, 1, z}]
%t A209769 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209769 TableForm[cv]
%t A209769 Flatten[%]    (* A209770 *)
%Y A209769 Cf. A209770, A208510.
%K A209769 nonn,tabl
%O A209769 1,3
%A A209769 _Clark Kimberling_, Mar 15 2012