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A210228 Triangle of coefficients of polynomials v(n,x) jointly generated with A210227; see the Formula section.

%I A210228 #4 Mar 30 2012 18:58:16
%S A210228 1,1,4,1,6,10,1,6,24,22,1,6,28,80,46,1,6,28,120,236,94,1,6,28,128,464,
%T A210228 640,190,1,6,28,128,568,1624,1636,382,1,6,28,128,584,2376,5224,4008,
%U A210228 766,1,6,28,128,584,2632,9240,15696,9516,1534,1,6,28,128,584
%N A210228 Triangle of coefficients of polynomials v(n,x) jointly generated with A210227; see the Formula section.
%C A210228 For a discussion and guide to related arrays, see A208510.
%F A210228 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210228 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A210228 where u(1,x)=1, v(1,x)=1.
%e A210228 First five rows:
%e A210228 1
%e A210228 1...4
%e A210228 1...6...10
%e A210228 1...6...24...22
%e A210228 1...6...28...80...46
%e A210228 First three polynomials v(n,x): 1, 1 + 4x , 1 + 6x + 19x^2.
%t A210228 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210228 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210228 v[n_, x_] := 2 x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210228 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210228 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210228 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210228 TableForm[cu]
%t A210228 Flatten[%]     (* A210227 *)
%t A210228 Table[Expand[v[n, x]], {n, 1, z}]
%t A210228 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210228 TableForm[cv]
%t A210228 Flatten[%]     (* A210228 *)
%Y A210228 Cf. A210227, A208510.
%K A210228 nonn,tabl
%O A210228 1,3
%A A210228 _Clark Kimberling_, Mar 20 2012