cp's OEIS Frontend

A210235 Triangle of coefficients of polynomials u(n,x) jointly generated with A210236; see the Formula section.

%I A210235 #4 Mar 30 2012 18:58:16
%S A210235 1,2,1,4,4,1,7,12,7,1,12,29,28,11,1,20,64,86,56,16,1,33,132,230,210,
%T A210235 101,22,1,54,261,560,662,451,169,29,1,88,500,1279,1860,1646,883,267,
%U A210235 37,1,143,936,2785,4819,5257,3682,1611,403,46,1,232,1721,5848
%N A210235 Triangle of coefficients of polynomials u(n,x) jointly generated with A210236; see the Formula section.
%C A210235 For a discussion and guide to related arrays, see A208510.
%F A210235 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210235 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210235 where u(1,x)=1, v(1,x)=1.
%e A210235 First five rows:
%e A210235 1
%e A210235 2....1
%e A210235 4....4....1
%e A210235 7....12...7....1
%e A210235 12...29...28...11...1
%e A210235 First three polynomials u(n,x): 1, 2 + x, 4 + 4x + x^2.
%t A210235 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210235 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210235 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210235 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210235 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210235 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210235 TableForm[cu]
%t A210235 Flatten[%]      (* A210235 *)
%t A210235 Table[Expand[v[n, x]], {n, 1, z}]
%t A210235 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210235 TableForm[cv]
%t A210235 Flatten[%]      (* A210236 *)
%Y A210235 Cf. A210236, A208510.
%K A210235 nonn,tabl
%O A210235 1,2
%A A210235 _Clark Kimberling_, Mar 20 2012