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A209158 Triangle of coefficients of polynomials u(n,x) jointly generated with A209159; see the Formula section.

%I A209158 #5 Mar 30 2012 18:58:15
%S A209158 1,2,1,3,5,3,4,11,13,5,5,19,35,31,11,6,29,73,101,73,21,7,41,131,247,
%T A209158 275,167,43,8,55,213,509,769,717,377,85,9,71,323,935,1787,2255,1811,
%U A209158 839,171,10,89,465,1581,3657,5829,6321,4461,1849,341,11,109,643
%N A209158 Triangle of coefficients of polynomials u(n,x) jointly generated with A209159; see the Formula section.
%C A209158 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209158 For a discussion and guide to related arrays, see A208510.
%F A209158 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209158 v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F A209158 where u(1,x)=1, v(1,x)=1.
%e A209158 First five rows:
%e A209158 1
%e A209158 2...1
%e A209158 3...5....5
%e A209158 4...11...13...5
%e A209158 5...19...35...31...11
%e A209158 First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 5x^2.
%t A209158 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209158 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209158 v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A209158 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209158 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209158 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209158 TableForm[cu]
%t A209158 Flatten[%]    (* A209158 *)
%t A209158 Table[Expand[v[n, x]], {n, 1, z}]
%t A209158 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209158 TableForm[cv]
%t A209158 Flatten[%]    (* A209159 *)
%Y A209158 Cf. A209159, A208510.
%K A209158 nonn,tabl
%O A209158 1,2
%A A209158 _Clark Kimberling_, Mar 07 2012