cp's OEIS Frontend

A210559 Triangle of coefficients of polynomials u(n,x) jointly generated with A210560; see the Formula section.

%I A210559 #5 Mar 30 2012 18:58:16
%S A210559 1,1,2,1,4,3,1,6,8,5,1,8,15,17,8,1,10,24,38,33,13,1,12,35,70,86,63,21,
%T A210559 1,14,48,115,180,187,117,34,1,16,63,175,330,437,390,214,55,1,18,80,
%U A210559 252,553,882,1007,791,386,89,1,20,99,348,868,1610,2219,2235,1567
%N A210559 Triangle of coefficients of polynomials u(n,x) jointly generated with A210560; see the Formula section.
%C A210559 For a discussion and guide to related arrays, see A208510.
%F A210559 u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A210559 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A210559 where u(1,x)=1, v(1,x)=1.
%e A210559 First five rows:
%e A210559 1
%e A210559 1...2
%e A210559 1...4...3
%e A210559 1...6...8....5
%e A210559 1...8...15...17...8
%e A210559 First three polynomials u(n,x): 1, 1 + 2x, 1 + 4x + 3x^2.
%t A210559 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210559 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210559 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A210559 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210559 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210559 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210559 TableForm[cu]
%t A210559 Flatten[%]  (* A210559 *)
%t A210559 Table[Expand[v[n, x]], {n, 1, z}]
%t A210559 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210559 TableForm[cv]
%t A210559 Flatten[%]  (* A210560 *)
%Y A210559 Cf. A210560, A208510.
%K A210559 nonn,tabl
%O A210559 1,3
%A A210559 _Clark Kimberling_, Mar 22 2012