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A209688 Triangle of coefficients of polynomials v(n,x) jointly generated with A115241; see the Formula section.

%I A209688 #5 Mar 30 2012 18:58:15
%S A209688 1,3,4,2,5,5,2,6,9,7,2,7,14,16,9,2,8,20,30,25,11,2,9,27,50,55,36,13,2,
%T A209688 10,35,77,105,91,49,15,2,11,44,112,182,196,140,64,17,2,12,54,156,294,
%U A209688 378,336,204,81,19,2,13,65,210,450,672,714,540,285,100,21,2
%N A209688 Triangle of coefficients of polynomials v(n,x) jointly generated with A115241; see the Formula section.
%C A209688 Alternating row sums: 1,3,2,2,2,2,2,2,2,2,2,2,...
%C A209688 For a discussion and guide to related arrays, see A208510.
%F A209688 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209688 v(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A209688 where u(1,x)=1, v(1,x)=1.
%e A209688 First five rows:
%e A209688 1
%e A209688 3...1
%e A209688 4...2...3
%e A209688 5...5...2
%e A209688 6...9...7...2
%e A209688 First three polynomials v(n,x): 1, 3 + x , 4 + 2x + 3x^2.
%t A209688 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209688 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t A209688 v[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A209688 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209688 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209688 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209688 TableForm[cu]
%t A209688 Flatten[%]    (* A115241 *)
%t A209688 Table[Expand[v[n, x]], {n, 1, z}]
%t A209688 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209688 TableForm[cv]
%t A209688 Flatten[%]   (* A209688 *)
%Y A209688 Cf. A115241, A208510.
%K A209688 nonn,tabf
%O A209688 1,2
%A A209688 _Clark Kimberling_, Mar 12 2012