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A208511 Triangle of coefficients of polynomials u(n,x) jointly generated with A208512; see the Formula section.

%I A208511 #5 Mar 30 2012 18:58:13
%S A208511 1,1,1,1,3,2,1,5,7,4,1,7,14,16,8,1,9,23,37,36,16,1,11,34,69,94,80,32,
%T A208511 1,13,47,114,195,232,176,64,1,15,62,174,354,528,560,384,128,1,17,79,
%U A208511 251,588,1041,1384,1328,832,256,1,19,98,347,916,1863,2938,3536
%N A208511 Triangle of coefficients of polynomials u(n,x) jointly generated with A208512; see the Formula section.
%F A208511 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208511 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A208511 where u(1,x)=1, v(1,x)=1.
%e A208511 First five rows:
%e A208511 1
%e A208511 1...1
%e A208511 1...3...2
%e A208511 1...5...7....4
%e A208511 1...7...14...16...8
%e A208511 First five polynomials u(n,x):
%e A208511 1
%e A208511 1 + x
%e A208511 1 + 3x + 2x^2
%e A208511 1 + 5x + 7x^2 + 4x^3
%e A208511 1 + 7x + 14x^2 + 16x^3 + 8x^4
%t A208511 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208511 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208511 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A208511 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208511 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208511 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208511 TableForm[cu]
%t A208511 Flatten[%]  (* A208511 *)
%t A208511 Table[Expand[v[n, x]], {n, 1, z}]
%t A208511 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208511 TableForm[cv]
%t A208511 Flatten[%]  (* A208512 *)
%Y A208511 Cf. A208511.
%K A208511 nonn,tabl
%O A208511 1,5
%A A208511 _Clark Kimberling_, Feb 28 2012