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A208515 Triangle of coefficients of polynomials v(n,x) jointly generated with A208514; see the Formula section.

%I A208515 #5 Mar 30 2012 18:58:13
%S A208515 1,1,2,1,2,3,1,2,4,5,1,2,5,8,8,1,2,6,11,15,13,1,2,7,14,23,28,21,1,2,8,
%T A208515 17,32,47,51,34,1,2,9,20,42,70,93,92,55,1,2,10,23,53,97,148,181,164,
%U A208515 89,1,2,11,26,65,128,217,306,346,290,144,1,2,12,29,78,163,301
%N A208515 Triangle of coefficients of polynomials v(n,x) jointly generated with A208514; see the Formula section.
%F A208515 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208515 v(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A208515 where u(1,x)=1, v(1,x)=1.
%e A208515 First five rows:
%e A208515 1
%e A208515 1...2
%e A208515 1...2...3
%e A208515 1...2...4...5
%e A208515 1...2...5...8...8
%e A208515 First five polynomials v(n,x):
%e A208515 1
%e A208515 1 + 2x
%e A208515 1 + 2x + 3x^2
%e A208515 1 + 2x + 4x^2 + 5x^3
%e A208515 1 + 2x + 5x^2 + 8x^3 + 8x^4
%t A208515 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208515 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208515 v[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A208515 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208515 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208515 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208515 TableForm[cu]
%t A208515 Flatten[%]    (* A208514 *)
%t A208515 Table[Expand[v[n, x]], {n, 1, z}]
%t A208515 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208515 TableForm[cv]
%t A208515 Flatten[%]    (* A208515 *)
%Y A208515 Cf. A208514.
%K A208515 nonn,tabl
%O A208515 1,3
%A A208515 _Clark Kimberling_, Feb 28 2012