A207630 - OEIS

%I #5 Mar 30 2012 18:58:13

%S 1,3,1,6,3,12,9,1,24,24,5,48,60,19,1,96,144,62,7,192,336,184,33,1,384,

%T 768,512,128,9,768,1728,1360,440,51,1,1536,3840,3488,1392,230,11,3072,

%U 8448,8704,4144,900,73,1,6144,18432,21248,11776,3192,376,13

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A207629; see the Formula section.

%F u(n,x)=u(n-1,x)+v(n-1,x),

%F v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,

%F where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 3....1

%e 6....3

%e 12...9....1

%e 24...24...5

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := u[n - 1, x] + v[n - 1, x]

%t v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1

%t Table[Factor[u[n, x]], {n, 1, z}]

%t Table[Factor[v[n, x]], {n, 1, z}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%]  (* A207629 *)

%t Table[Expand[v[n, x]], {n, 1, z}]

%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

%t TableForm[cv]

%t Flatten[%]  (* A207630 *)

%Y Cf. A207629.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_, Feb 23 2012