cp's OEIS Frontend

A209751 Triangle of coefficients of polynomials u(n,x) jointly generated with A209752; see the Formula section.

%I A209751 #6 Mar 30 2012 18:58:15
%S A209751 1,1,2,2,5,4,2,10,15,8,3,14,35,39,16,3,22,63,108,95,32,4,27,109,235,
%T A209751 309,223,64,4,38,160,454,782,838,511,128,5,44,242,770,1688,2408,2183,
%U A209751 1151,256,5,58,322,1264,3226,5776,7009,5512,2559,512,6,65,450
%N A209751 Triangle of coefficients of polynomials u(n,x) jointly generated with A209752; see the Formula section.
%C A209751 Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...
%C A209751 For a discussion and guide to related arrays, see A208510.
%F A209751 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209751 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A209751 where u(1,x)=1, v(1,x)=1.
%e A209751 First five rows:
%e A209751 1
%e A209751 1...2
%e A209751 2...5....4
%e A209751 2...10...15...8
%e A209751 3...14...35...39...16
%e A209751 First three polynomials u(n,x): 1, 1 + 2x, 2 + 5x + 4x^2.
%t A209751 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209751 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209751 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209751 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209751 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209751 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209751 TableForm[cu]
%t A209751 Flatten[%]    (* A209751 *)
%t A209751 Table[Expand[v[n, x]], {n, 1, z}]
%t A209751 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209751 TableForm[cv]
%t A209751 Flatten[%]    (* A209752 *)
%Y A209751 Cf. A209752, A208510.
%K A209751 nonn,tabl
%O A209751 1,3
%A A209751 _Clark Kimberling_, Mar 14 2012