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A209163 Triangle of coefficients of polynomials v(n,x) jointly generated with A209162; see the Formula section.

%I A209163 #5 Mar 30 2012 18:58:15
%S A209163 1,2,3,3,9,5,4,20,26,11,5,38,82,71,21,6,65,204,279,176,43,7,103,439,
%T A209163 849,845,425,85,8,154,854,2192,3050,2386,990,171,9,220,1540,5034,9174,
%U A209163 9940,6396,2267,341,10,303,2616,10578,24232,34102,30228,16521
%N A209163 Triangle of coefficients of polynomials v(n,x) jointly generated with A209162; see the Formula section.
%C A209163 Alternating row sums: 1,-1,-1,-1,-,1-,1-,1,-1,...
%C A209163 For a discussion and guide to related arrays, see A208510.
%F A209163 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209163 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209163 where u(1,x)=1, v(1,x)=1.
%e A209163 First five rows:
%e A209163 1
%e A209163 2...3
%e A209163 3...9...5
%e A209163 4...20...26...11
%e A209163 5...38...82...71...21
%e A209163 First three polynomials v(n,x): 1, 2 + 3x, 3 + 9x + 5x^2.
%t A209163 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209163 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209163 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209163 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209163 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209163 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209163 TableForm[cu]
%t A209163 Flatten[%]    (* A209162 *)
%t A209163 Table[Expand[v[n, x]], {n, 1, z}]
%t A209163 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209163 TableForm[cv]
%t A209163 Flatten[%]    (* A209163 *)
%Y A209163 Cf. A209162, A208510.
%K A209163 nonn,tabl
%O A209163 1,2
%A A209163 _Clark Kimberling_, Mar 07 2012