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A209143 Triangle of coefficients of polynomials u(n,x) jointly generated with A209144; see the Formula section.

%I A209143 #7 Mar 30 2012 18:58:15
%S A209143 1,2,1,5,4,11,11,1,23,28,6,47,68,23,1,95,160,74,8,191,368,216,39,1,
%T A209143 383,832,592,152,10,767,1856,1552,520,59,1,1535,4096,3936,1632,270,12,
%U A209143 3071,8960,9728,4816,1060,83,1,6143,19456,23552,13568,3752,436
%N A209143 Triangle of coefficients of polynomials u(n,x) jointly generated with A209144; see the Formula section.
%C A209143 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209143 For a discussion and guide to related arrays, see A208510.
%F A209143 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209143 v(n,x)=u(n-1,x)+v(n-1,x) + 1,
%F A209143 where u(1,x)=1, v(1,x)=1.
%e A209143 First five rows:
%e A209143 1
%e A209143 2....1
%e A209143 5....4
%e A209143 11...11...1
%e A209143 23...28...6
%e A209143 First three polynomials u(n,x):  1, 2 + x, 5 + 4x
%t A209143 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209143 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209143 v[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A209143 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209143 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209143 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209143 TableForm[cu]
%t A209143 Flatten[%]    (* A209143 *)
%t A209143 Table[Expand[v[n, x]], {n, 1, z}]
%t A209143 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209143 TableForm[cv]
%t A209143 Flatten[%]    (* A209144 *)
%Y A209143 Cf. A209144, A208510.
%K A209143 nonn,tabf
%O A209143 1,2
%A A209143 _Clark Kimberling_, Mar 06 2012