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A209776 Triangle of coefficients of polynomials v(n,x) jointly generated with A209773; see the Formula section.

%I A209776 #5 Mar 30 2012 18:58:15
%S A209776 1,3,2,5,8,4,9,22,22,8,15,52,78,56,16,25,112,226,242,136,32,41,228,
%T A209776 580,828,692,320,64,67,446,1374,2456,2726,1872,736,128,109,848,3074,
%U A209776 6612,9158,8336,4864,1664,256,177,1578,6590,16590,27564,31250
%N A209776 Triangle of coefficients of polynomials v(n,x) jointly generated with A209773; see the Formula section.
%C A209776 Alternating row sums: 1,1,1,1,1,1,1,1,...
%C A209776 For a discussion and guide to related arrays, see A208510.
%F A209776 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209776 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A209776 where u(1,x)=1, v(1,x)=1.
%e A209776 First five rows:
%e A209776 1
%e A209776 3....2
%e A209776 5....8....4
%e A209776 9....22...22...8
%e A209776 15...52...78...56...16
%e A209776 First three polynomials v(n,x): 1, 3 + 2x , 5 + 8x + 4x^2.
%t A209776 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209776 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209776 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209776 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209776 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209776 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209776 TableForm[cu]
%t A209776 Flatten[%]    (* A209775 *)
%t A209776 Table[Expand[v[n, x]], {n, 1, z}]
%t A209776 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209776 TableForm[cv]
%t A209776 Flatten[%]    (* A209776 *)
%Y A209776 Cf. A209675, A208510.
%K A209776 nonn,tabl
%O A209776 1,2
%A A209776 _Clark Kimberling_, Mar 15 2012