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

%I A209162 #5 Mar 30 2012 18:58:15
%S A209162 1,2,1,4,6,3,7,18,17,5,11,42,63,42,11,16,85,183,195,103,21,22,156,452,
%T A209162 678,558,240,43,29,266,994,1966,2252,1510,553,85,37,428,2002,5012,
%U A209162 7494,6946,3929,1246,171,46,657,3762,11586,21702,26060,20265,9909
%N A209162 Triangle of coefficients of polynomials u(n,x) jointly generated with A209163; see the Formula section.
%C A209162 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209162 For a discussion and guide to related arrays, see A208510.
%F A209162 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209162 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209162 where u(1,x)=1, v(1,x)=1.
%e A209162 First five rows:
%e A209162 1
%e A209162 2....1
%e A209162 4....6....3
%e A209162 7....18...17...5
%e A209162 11...42...63...42...11
%e A209162 First three polynomials v(n,x): 1, 2 + x, 4 + 6x + 3x^2.
%t A209162 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209162 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209162 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209162 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209162 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209162 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209162 TableForm[cu]
%t A209162 Flatten[%]    (* A209162 *)
%t A209162 Table[Expand[v[n, x]], {n, 1, z}]
%t A209162 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209162 TableForm[cv]
%t A209162 Flatten[%]    (* A209163 *)
%Y A209162 Cf. A209163, A208510.
%K A209162 nonn,tabl
%O A209162 1,2
%A A209162 _Clark Kimberling_, Mar 07 2012