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A208753 Triangle of coefficients of polynomials u(n,x) jointly generated with A208754; see the Formula section.

%I A208753 #5 Mar 30 2012 18:58:14
%S A208753 1,1,2,1,8,1,18,4,1,32,24,1,50,80,8,1,72,200,64,1,98,420,280,16,1,128,
%T A208753 784,896,160,1,162,1344,2352,864,32,1,200,2160,5376,3360,384,1,242,
%U A208753 3300,11088,10560,2464,64,1,288,4840,21120,28512,11264,896,1
%N A208753 Triangle of coefficients of polynomials u(n,x) jointly generated with A208754; see the Formula section.
%C A208753 For a discussion and guide to related arrays, see A208510.
%F A208753 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208753 v(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A208753 where u(1,x)=1, v(1,x)=1.
%e A208753 First five rows:
%e A208753 1
%e A208753 1...2
%e A208753 1...8
%e A208753 1...18...4
%e A208753 1...32...24
%e A208753 First five polynomials u(n,x):
%e A208753 1
%e A208753 1 + 2x
%e A208753 1 + 8x
%e A208753 1 + 18x + 4x^2
%e A208753 1 + 32x + 24x^2
%t A208753 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208753 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208753 v[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A208753 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208753 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208753 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208753 TableForm[cu]
%t A208753 Flatten[%]    (* A208753 *)
%t A208753 Table[Expand[v[n, x]], {n, 1, z}]
%t A208753 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208753 TableForm[cv]
%t A208753 Flatten[%]    (* A208754 *)
%Y A208753 Cf. A208754, A208510.
%K A208753 nonn,tabf
%O A208753 1,3
%A A208753 _Clark Kimberling_, Mar 03 2012