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A208523 Triangle of coefficients of polynomials v(n,x) jointly generated with A208522; see the Formula section.

%I A208523 #5 Mar 30 2012 18:58:13
%S A208523 1,1,3,1,3,5,1,3,7,11,1,3,9,19,21,1,3,11,27,43,43,1,3,13,35,69,103,85,
%T A208523 1,3,15,43,99,183,231,171,1,3,17,51,133,283,449,523,341,1,3,19,59,171,
%U A208523 403,747,1107,1155,683,1,3,21,67,213,543,1133,1971,2637,2543
%N A208523 Triangle of coefficients of polynomials v(n,x) jointly generated with A208522; see the Formula section.
%F A208523 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208523 v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F A208523 where u(1,x)=1, v(1,x)=1.
%e A208523 First five rows:
%e A208523 1
%e A208523 1...3
%e A208523 1...3...5
%e A208523 1...3...7...11
%e A208523 1...3...9...19...21
%e A208523 First five polynomials v(n,x):
%e A208523 1
%e A208523 1 + 3x
%e A208523 1 + 3x + 5x^2
%e A208523 1 + 3x + 7x^2 + 11x^3
%e A208523 1 + 3x + 9x^2 + 19x^3 + 21x^4
%t A208523 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208523 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208523 v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A208523 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208523 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208523 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208523 TableForm[cu]
%t A208523 Flatten[%]    (* A208522 *)
%t A208523 Table[Expand[v[n, x]], {n, 1, z}]
%t A208523 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208523 TableForm[cv]
%t A208523 Flatten[%]    (* A208523 *)
%Y A208523 Cf. A208522.
%K A208523 nonn,tabl
%O A208523 1,3
%A A208523 _Clark Kimberling_, Feb 29 2012