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A208913 Triangle of coefficients of polynomials u(n,x) jointly generated with A208914; see the Formula section.

%I A208913 #5 Mar 30 2012 18:58:14
%S A208913 1,1,2,1,6,4,1,12,12,8,1,20,24,40,16,1,30,40,120,80,32,1,42,60,280,
%T A208913 240,224,64,1,56,84,560,560,896,448,128,1,72,112,1008,1120,2688,1792,
%U A208913 1152,256,1,90,144,1680,2016,6720,5376,5760,2304,512,1,110,180
%N A208913 Triangle of coefficients of polynomials u(n,x) jointly generated with A208914; see the Formula section.
%C A208913 For a discussion and guide to related arrays, see A208510.
%F A208913 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208913 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A208913 where u(1,x)=1, v(1,x)=1.
%e A208913 First five rows:
%e A208913 1
%e A208913 1...2
%e A208913 1...6....4
%e A208913 1...12...12...8
%e A208913 1...20...24...40...16
%e A208913 First five polynomials u(n,x):
%e A208913 1
%e A208913 1 + 2x
%e A208913 1 + 6x + 4x^2
%e A208913 1 + 12x + 12x^2 + 8x^3
%e A208913 1 + 20x + 24x^2 + 40x^3 + 16x^4
%t A208913 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208913 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A208913 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208913 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208913 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208913 TableForm[cu]
%t A208913 Flatten[%]    (* A208913 *)
%t A208913 Table[Expand[v[n, x]], {n, 1, z}]
%t A208913 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208913 TableForm[cv]
%t A208913 Flatten[%]    (* A208914 *)
%Y A208913 Cf. A208914, A208510.
%K A208913 nonn,tabl
%O A208913 1,3
%A A208913 _Clark Kimberling_, Mar 03 2012