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A209154 Triangle of coefficients of polynomials u(n,x) jointly generated with A209157; see the Formula section.

%I A209154 #5 Mar 30 2012 18:58:15
%S A209154 1,2,1,4,5,2,7,14,10,2,11,32,36,18,4,16,65,104,82,32,4,22,121,258,282,
%T A209154 168,52,8,29,210,574,820,676,328,88,8,37,344,1176,2116,2264,1504,608,
%U A209154 136,16,46,537,2256,4980,6640,5672,3136,1096,224,16,56,805
%N A209154 Triangle of coefficients of polynomials u(n,x) jointly generated with A209157; see the Formula section.
%C A209154 Last number in each row is a power of 2.
%C A209154 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209154 For a discussion and guide to related arrays, see A208510.
%F A209154 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209154 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A209154 where u(1,x)=1, v(1,x)=1.
%e A209154 First five rows:
%e A209154 1
%e A209154 2....1
%e A209154 4....5....2
%e A209154 7....14...10...2
%e A209154 11...32...36...18...4
%e A209154 First three polynomials v(n,x): 1, 2 + x, 4 + 5x + 2x^2.
%t A209154 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209154 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209154 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A209154 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209154 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209154 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209154 TableForm[cu]
%t A209154 Flatten[%]    (* A209154 *)
%t A209154 Table[Expand[v[n, x]], {n, 1, z}]
%t A209154 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209154 TableForm[cv]
%t A209154 Flatten[%]    (* A209157 *)
%Y A209154 Cf. A209157, A208510.
%K A209154 nonn,tabl
%O A209154 1,2
%A A209154 _Clark Kimberling_, Mar 07 2012