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A209146 Triangle of coefficients of polynomials u(n,x) jointly generated with A209147; see the Formula section.

%I A209146 #5 Mar 30 2012 18:58:15
%S A209146 1,2,1,4,5,2,7,13,11,4,12,29,34,24,8,20,60,90,85,52,16,33,118,215,255,
%T A209146 206,112,32,54,225,481,680,683,488,240,64,88,419,1028,1682,1994,1760,
%U A209146 1136,512,128,143,767,2122,3937,5361,5553,4408,2608,1088,256
%N A209146 Triangle of coefficients of polynomials u(n,x) jointly generated with A209147; see the Formula section.
%C A209146 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209146 For a discussion and guide to related arrays, see A208510.
%F A209146 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209146 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A209146 where u(1,x)=1, v(1,x)=1.
%e A209146 First five rows:
%e A209146 1
%e A209146 2...1
%e A209146 4...5...2
%e A209146 7...13...11...4
%e A209146 12...29...34...24...8
%e A209146 First three polynomials v(n,x): 1, 2 + x, 4 + 5x + 2x^2.
%t A209146 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209146 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209146 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209146 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209146 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209146 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209146 TableForm[cu]
%t A209146 Flatten[%]    (* A209146 *)
%t A209146 Table[Expand[v[n, x]], {n, 1, z}]
%t A209146 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209146 TableForm[cv]
%t A209146 Flatten[%]    (* A209147 *)
%Y A209146 Cf. A209146, A208510.
%K A209146 nonn,tabl
%O A209146 1,2
%A A209146 _Clark Kimberling_, Mar 06 2012