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