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A209773 Triangle of coefficients of polynomials u(n,x) jointly generated with A209774; see the Formula section.

%I A209773 #5 Mar 30 2012 18:58:15
%S A209773 1,1,2,2,6,5,2,11,21,13,3,17,48,67,34,3,25,92,188,206,89,4,33,154,422,
%T A209773 684,619,233,4,44,238,809,1756,2365,1829,610,5,54,348,1411,3801,6833,
%U A209773 7882,5334,1597,5,68,484,2285,7369,16471,25302,25549,15393
%N A209773 Triangle of coefficients of polynomials u(n,x) jointly generated with A209774; see the Formula section.
%C A209773 Last term in row n: F(2n+1), where F=A000045, the Fibonacci numbers
%C A209773 For a discussion and guide to related arrays, see A208510.
%F A209773 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209773 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A209773 where u(1,x)=1, v(1,x)=1.
%e A209773 First five rows:
%e A209773 1
%e A209773 1...2
%e A209773 2...6....5
%e A209773 2...11...21...13
%e A209773 3...17...48...67...34
%e A209773 First three polynomials u(n,x): 1, 1 + 2x, 2 + 6x + 5x^2.
%t A209773 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209773 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209773 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209773 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209773 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209773 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209773 TableForm[cu]
%t A209773 Flatten[%]    (* A209773 *)
%t A209773 Table[Expand[v[n, x]], {n, 1, z}]
%t A209773 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209773 TableForm[cv]
%t A209773 Flatten[%]    (* A209774 *)
%Y A209773 Cf. A209774, A208510.
%K A209773 nonn,tabl
%O A209773 1,3
%A A209773 _Clark Kimberling_, Mar 15 2012