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A210753 Triangle of coefficients of polynomials u(n,x) jointly generated with A210754; see the Formula section.

%I A210753 #5 Mar 30 2012 18:58:17
%S A210753 1,2,2,3,7,4,4,16,20,8,5,30,61,52,16,6,50,146,198,128,32,7,77,301,575,
%T A210753 584,304,64,8,112,560,1408,1992,1616,704,128,9,156,966,3060,5641,6328,
%U A210753 4272,1600,256,10,210,1572,6084,14002,20330,18880,10912,3584
%N A210753 Triangle of coefficients of polynomials u(n,x) jointly generated with A210754; see the Formula section.
%C A210753 Row n starts with n and ends with 2^(n-1).
%C A210753 Row sums: A007070
%C A210753 Alternating row sums: 1,0,0,0,0,0,0,0,0,....
%C A210753 For a discussion and guide to related arrays, see A208510.
%F A210753 u(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A210753 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210753 where u(1,x)=1, v(1,x)=1.
%e A210753 First five rows:
%e A210753 1
%e A210753 2...2
%e A210753 3...7....4
%e A210753 4...16...20...8
%e A210753 5...30...61...52...16
%e A210753 First three polynomials u(n,x): 1, 2 + 2x, 3 + 7x + 4x^2.
%t A210753 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210753 u[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210753 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210753 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210753 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210753 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210753 TableForm[cu]
%t A210753 Flatten[%]    (* A210753 *)
%t A210753 Table[Expand[v[n, x]], {n, 1, z}]
%t A210753 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210753 TableForm[cv]
%t A210753 Flatten[%]    (* A210754 *)
%t A210753 Table[u[n, x] /. x -> 1, {n, 1, z}] (* A007070 *)
%t A210753 Table[v[n, x] /. x -> 1, {n, 1, z}] (* A035344 *)
%Y A210753 Cf. A210754, A208510.
%K A210753 nonn,tabl
%O A210753 1,2
%A A210753 _Clark Kimberling_, Mar 25 2012