cp's OEIS Frontend

A209754 Triangle of coefficients of polynomials v(n,x) jointly generated with A209753; see the Formula section.

%I A209754 #5 Mar 30 2012 18:58:15
%S A209754 1,3,1,5,6,1,9,16,10,1,15,39,38,15,1,25,84,117,76,21,1,41,172,308,286,
%T A209754 136,28,1,67,337,744,894,612,225,36,1,109,642,1685,2496,2228,1191,351,
%U A209754 45,1,177,1196,3646,6423,7088,4978,2157,523,55,1,287,2191
%N A209754 Triangle of coefficients of polynomials v(n,x) jointly generated with A209753; see the Formula section.
%C A209754 For a discussion and guide to related arrays, see A208510.
%F A209754 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209754 v(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209754 where u(1,x)=1, v(1,x)=1.
%e A209754 First five rows:
%e A209754 1
%e A209754 3....1
%e A209754 5....6....1
%e A209754 9....16...10...1
%e A209754 15...39...38...15...1
%e A209754 First three polynomials v(n,x): 1, 3 + x , 5 + 6x + x^2.
%t A209754 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209754 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209754 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209754 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209754 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209754 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209754 TableForm[cu]
%t A209754 Flatten[%]    (* A209753 *)
%t A209754 Table[Expand[v[n, x]], {n, 1, z}]
%t A209754 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209754 TableForm[cv]
%t A209754 Flatten[%]    (* A209754 *)
%Y A209754 Cf. A209653, A208510.
%K A209754 nonn,tabl
%O A209754 1,2
%A A209754 _Clark Kimberling_, Mar 14 2012