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A209555 Triangle of coefficients of polynomials u(n,x) jointly generated with A209556; see the Formula section.

%I A209555 #6 Mar 30 2012 18:58:15
%S A209555 1,1,1,2,2,1,2,5,3,1,3,6,9,4,1,3,11,13,14,5,1,4,12,28,24,20,6,1,4,19,
%T A209555 34,59,40,27,7,1,5,20,62,80,110,62,35,8,1,5,29,70,164,166,188,91,44,9,
%U A209555 1,6,30,115,200,376,314,301,128,54,10,1,6,41,125,365,496,776
%N A209555 Triangle of coefficients of polynomials u(n,x) jointly generated with A209556; see the Formula section.
%C A209555 For a discussion and guide to related arrays, see A208510.
%F A209555 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209555 v(n,x)=u(n-1,x)+x*v(n-1,x) +1,
%F A209555 where u(1,x)=1, v(1,x)=1.
%e A209555 First five rows:
%e A209555 1
%e A209555 1...1
%e A209555 2...2...1
%e A209555 2...5...3...1
%e A209555 3...6...9...4...1
%e A209555 First three polynomials v(n,x): 1, 1 + x, 2 + 2x + x^2.
%t A209555 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209555 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209555 v[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
%t A209555 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209555 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209555 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209555 TableForm[cu]
%t A209555 Flatten[%]    (* A209555 *)
%t A209555 Table[Expand[v[n, x]], {n, 1, z}]
%t A209555 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209555 TableForm[cv]
%t A209555 Flatten[%]    (* A209556 *)
%Y A209555 Cf. A209556, A208510.
%K A209555 nonn,tabl
%O A209555 1,4
%A A209555 _Clark Kimberling_, Mar 10 2012