cp's OEIS Frontend

A209747 Triangle of coefficients of polynomials u(n,x) jointly generated with A209748; see the Formula section.

%I A209747 #8 Mar 30 2012 18:58:15
%S A209747 1,1,2,3,4,2,5,10,6,2,9,20,18,8,2,15,40,44,28,10,2,25,76,102,80,40,12,
%T A209747 2,41,142,222,210,130,54,14,2,67,260,466,512,380,196,70,16,2,109,470,
%U A209747 948,1188,1022,630,280,88,18,2,177,840,1884,2648,2590,1848,980
%N A209747 Triangle of coefficients of polynomials u(n,x) jointly generated with A209748; see the Formula section.
%C A209747 Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...
%C A209747 For a discussion and guide to related arrays, see A208510.
%F A209747 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209747 v(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A209747 where u(1,x)=1, v(1,x)=1.
%e A209747 First five rows:
%e A209747 1
%e A209747 1...2
%e A209747 3...4....2
%e A209747 5...10...6....2
%e A209747 9...20...18...8...2
%e A209747 First three polynomials u(n,x): 1, 1 + 2x, 3 + 4x + 2x^2.
%t A209747 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209747 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209747 v[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A209747 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209747 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209747 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209747 TableForm[cu]
%t A209747 Flatten[%]    (* A209747 *)
%t A209747 Table[Expand[v[n, x]], {n, 1, z}]
%t A209747 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209747 TableForm[cv]
%t A209747 Flatten[%]    (* A209748 *)
%Y A209747 Cf. A209748, A208510.
%K A209747 nonn,tabl
%O A209747 1,3
%A A209747 _Clark Kimberling_, Mar 13 2012