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A209562 Triangle of coefficients of polynomials v(n,x) jointly generated with A209561; see the Formula section.

%I A209562 #6 Mar 30 2012 18:58:15
%S A209562 1,2,1,3,2,1,4,4,3,1,5,7,7,4,1,6,11,14,11,5,1,7,16,25,25,16,6,1,8,22,
%T A209562 41,50,41,22,7,1,9,29,63,91,91,63,29,8,1,10,37,92,154,182,154,92,37,9,
%U A209562 1,11,46,129,246,336,336,246,129,46,10,1,12,56,175,375,582,672
%N A209562 Triangle of coefficients of polynomials v(n,x) jointly generated with A209561; see the Formula section.
%C A209562 Alternating row sums: 1,1,2,2,2,2,2,2,2,2,2,2,2,2,...
%C A209562 For a discussion and guide to related arrays, see A208510.
%F A209562 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209562 v(n,x)=x*u(n-1,x)+v(n-1,x) +1,
%F A209562 where u(1,x)=1, v(1,x)=1.
%e A209562 First five rows:
%e A209562 1
%e A209562 1...1
%e A209562 3...2...1
%e A209562 4...4...3...1
%e A209562 5...7...7...4...1
%e A209562 First three polynomials v(n,x): 1, 3 + x , 5 + 5x + x^2.
%t A209562 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209562 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209562 v[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A209562 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209562 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209562 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209562 TableForm[cu]
%t A209562 Flatten[%]   (* A209561 *)
%t A209562 Table[Expand[v[n, x]], {n, 1, z}]
%t A209562 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209562 TableForm[cv]
%t A209562 Flatten[%]   (* A209562 *)
%Y A209562 Cf. A209561, A208510.
%K A209562 nonn,tabl
%O A209562 1,2
%A A209562 _Clark Kimberling_, Mar 10 2012