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A209560 Triangle of coefficients of polynomials v(n,x) jointly generated with A209559; see the Formula section.

%I A209560 #5 Mar 30 2012 18:58:15
%S A209560 1,3,1,5,5,1,9,12,7,1,15,29,22,9,1,25,61,66,35,11,1,41,124,166,125,51,
%T A209560 13,1,67,241,394,365,211,70,15,1,109,457,877,988,701,329,92,17,1,177,
%U A209560 848,1877,2472,2129,1225,484,117,19,1,287,1549,3884,5880,5909
%N A209560 Triangle of coefficients of polynomials v(n,x) jointly generated with A209559; see the Formula section.
%C A209560 For a discussion and guide to related arrays, see A208510.
%F A209560 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209560 v(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209560 where u(1,x)=1, v(1,x)=1.
%e A209560 First five rows:
%e A209560 1
%e A209560 3....1
%e A209560 5....5....1
%e A209560 9....12...7....1
%e A209560 15...29...22...9...1
%e A209560 First three polynomials v(n,x): 1, 3 + x , 5 + 5x + x^2.
%t A209560 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209560 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209560 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209560 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209560 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209560 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209560 TableForm[cu]
%t A209560 Flatten[%]   (* A209559 *)
%t A209560 Table[Expand[v[n, x]], {n, 1, z}]
%t A209560 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209560 TableForm[cv]
%t A209560 Flatten[%]   (* A209560 *)
%Y A209560 Cf. A209559, A208510.
%K A209560 nonn,tabl
%O A209560 1,2
%A A209560 _Clark Kimberling_, Mar 10 2012