cp's OEIS Frontend

A208918 Triangle of coefficients of polynomials v(n,x) jointly generated with A208917; see the Formula section.

%I A208918 #5 Mar 30 2012 18:58:14
%S A208918 1,1,4,1,4,12,1,4,16,40,1,4,20,64,128,1,4,24,88,240,416,1,4,28,112,
%T A208918 368,896,1344,1,4,32,136,512,1504,3264,4352,1,4,36,160,672,2240,5952,
%U A208918 11776,14080,1,4,40,184,848,3104,9472,23168,41984,45568,1,4,44
%N A208918 Triangle of coefficients of polynomials v(n,x) jointly generated with A208917; see the Formula section.
%C A208918 For a discussion and guide to related arrays, see A208510.
%F A208918 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208918 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A208918 where u(1,x)=1, v(1,x)=1.
%e A208918 First five rows:
%e A208918 1
%e A208918 1...4
%e A208918 1...4...12
%e A208918 1...4...16...40
%e A208918 1...4...20...64...128
%e A208918 First five polynomials v(n,x):
%e A208918 1
%e A208918 1 + 4x
%e A208918 1 + 4x + 12x^2
%e A208918 1 + 4x + 16x^2 + 40x^3
%e A208918 1 + 4x + 20x^2 + 64x^3 + 128x^4
%t A208918 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208918 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208918 v[n_, x_] := 2 x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A208918 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208918 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208918 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208918 TableForm[cu]
%t A208918 Flatten[%]    (* A208917 *)
%t A208918 Table[Expand[v[n, x]], {n, 1, z}]
%t A208918 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208918 TableForm[cv]
%t A208918 Flatten[%]    (* A208918 *)
%Y A208918 Cf. A208917, A208510.
%K A208918 nonn,tabl
%O A208918 1,3
%A A208918 _Clark Kimberling_, Mar 04 2012