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A210600 Triangle of coefficients of polynomials u(n,x) jointly generated with A210601; see the Formula section.

%I A210600 #5 Mar 30 2012 18:58:17
%S A210600 1,2,2,4,7,4,7,19,20,8,12,44,69,52,16,20,94,196,218,128,32,33,190,497,
%T A210600 731,632,304,64,54,370,1167,2139,2440,1728,704,128,88,701,2594,5701,
%U A210600 8081,7544,4528,1600,256,143,1301,5533,14195,24062,27874,22048
%N A210600 Triangle of coefficients of polynomials u(n,x) jointly generated with A210601; see the Formula section.
%C A210600 Alternating row sums: 1,0,1,0,1,0,1,0,...
%C A210600 For a discussion and guide to related arrays, see A208510.
%F A210600 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A210600 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210600 where u(1,x)=1, v(1,x)=1.
%e A210600 First five rows:
%e A210600 1
%e A210600 2....2
%e A210600 4....7....4
%e A210600 7....19...20...8
%e A210600 12...44...69...52...16
%e A210600 First three polynomials u(n,x): 1, 2+ 2x, 4 + 7x + 4x^2.
%t A210600 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210600 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210600 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210600 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210600 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210600 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210600 TableForm[cu]
%t A210600 Flatten[%]    (* A210600 *)
%t A210600 Table[Expand[v[n, x]], {n, 1, z}]
%t A210600 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210600 TableForm[cv]
%t A210600 Flatten[%]    (* A210601 *)
%Y A210600 Cf. A210601, A208510.
%K A210600 nonn,tabl
%O A210600 1,2
%A A210600 _Clark Kimberling_, Mar 24 2012