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A209160 Triangle of coefficients of polynomials u(n,x) jointly generated with A209161; see the Formula section.

%I A209160 #5 Mar 30 2012 18:58:15
%S A209160 1,2,1,3,6,4,4,13,20,10,5,22,52,62,28,6,33,104,192,192,76,7,46,180,
%T A209160 444,680,584,208,8,61,284,870,1776,2328,1760,568,9,78,420,1530,3876,
%U A209160 6768,7776,5256,1552,10,97,592,2492,7504,16260,24864,25464,15584
%N A209160 Triangle of coefficients of polynomials u(n,x) jointly generated with A209161; see the Formula section.
%C A209160 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209160 For a discussion and guide to related arrays, see A208510.
%F A209160 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209160 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A209160 where u(1,x)=1, v(1,x)=1.
%e A209160 First five rows:
%e A209160 1
%e A209160 2...1
%e A209160 3...6....4
%e A209160 4...13...20...10
%e A209160 5...22...52...62...28
%e A209160 First three polynomials v(n,x): 1, 2 + x, 3 + 6x + 4x^2.
%t A209160 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209160 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209160 v[n_, x_] := 2 x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209160 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209160 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209160 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209160 TableForm[cu]
%t A209160 Flatten[%]    (* A209160 *)
%t A209160 Table[Expand[v[n, x]], {n, 1, z}]
%t A209160 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209160 TableForm[cv]
%t A209160 Flatten[%]    (* A209161 *)
%Y A209160 Cf. A209161, A208510.
%K A209160 nonn,tabl
%O A209160 1,2
%A A209160 _Clark Kimberling_, Mar 07 2012