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A209168 Triangle of coefficients of polynomials u(n,x) jointly generated with A209169; see the Formula section.

%I A209168 #5 Mar 30 2012 18:58:15
%S A209168 1,2,1,4,6,3,7,16,17,7,12,37,56,47,17,20,78,154,182,128,41,33,156,378,
%T A209168 574,565,344,99,54,301,864,1590,1995,1697,915,239,88,566,1877,4048,
%U A209168 6118,6605,4973,2413,577,143,1044,3927,9693,17073,22128,21093
%N A209168 Triangle of coefficients of polynomials u(n,x) jointly generated with A209169; see the Formula section.
%C A209168 Row n begins with F(n+2)-1, where F=A000045 (Fibonacci numbers).
%C A209168 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209168 For a discussion and guide to related arrays, see A208510.
%F A209168 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209168 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A209168 where u(1,x)=1, v(1,x)=1.
%e A209168 First five rows:
%e A209168 1
%e A209168 2....1
%e A209168 4....6....3
%e A209168 7....16...17...7
%e A209168 12...37...56...47...17
%e A209168 First three polynomials v(n,x): 1, 2 + x, 4 + 6x + 3x^2.
%t A209168 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209168 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209168 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209168 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209168 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209168 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209168 TableForm[cu]
%t A209168 Flatten[%]    (* A209168 *)
%t A209168 Table[Expand[v[n, x]], {n, 1, z}]
%t A209168 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209168 TableForm[cv]
%t A209168 Flatten[%]    (* A209169 *)
%Y A209168 Cf. A209169, A208510.
%K A209168 nonn,tabl
%O A209168 1,2
%A A209168 _Clark Kimberling_, Mar 08 2012