A210752 - OEIS

%I #5 Mar 30 2012 18:58:17

%S 1,2,3,3,8,8,4,15,27,21,5,24,61,86,55,6,35,114,227,265,144,7,48,190,

%T 484,799,798,377,8,63,293,905,1910,2703,2362,987,9,80,427,1546,3951,

%U 7150,8874,6898,2584,10,99,596,2471,7391,16188,25711,28455,19929

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210751; see the Formula section.

%C Row n starts with n and ends with F(2n), where F=A000045 (Fibonacci numbers).

%C For a discussion and guide to related arrays, see A208510.

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

%F v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,

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

%e First five rows:

%e 1

%e 2...3

%e 3...8....8

%e 4...15...27...21

%e 5...24...61...86...55

%e First three polynomials v(n,x): 1, 2 + 3x, 3 + 8x +8x^2

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

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

%t v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;

%t Table[Expand[u[n, x]], {n, 1, z/2}]

%t Table[Expand[v[n, x]], {n, 1, z/2}]

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

%t TableForm[cu]

%t Flatten[%]    (* A210751 *)

%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[%]    (* A210752 *)

%Y Cf. A210751, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 25 2012