cp's OEIS Frontend

A210752 Triangle of coefficients of polynomials v(n,x) jointly generated with A210751; see the Formula section.

%I A210752 #5 Mar 30 2012 18:58:17
%S A210752 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 A210752 484,799,798,377,8,63,293,905,1910,2703,2362,987,9,80,427,1546,3951,
%U A210752 7150,8874,6898,2584,10,99,596,2471,7391,16188,25711,28455,19929
%N A210752 Triangle of coefficients of polynomials v(n,x) jointly generated with A210751; see the Formula section.
%C A210752 Row n starts with n and ends with F(2n), where F=A000045 (Fibonacci numbers).
%C A210752 For a discussion and guide to related arrays, see A208510.
%F A210752 u(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A210752 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A210752 where u(1,x)=1, v(1,x)=1.
%e A210752 First five rows:
%e A210752 1
%e A210752 2...3
%e A210752 3...8....8
%e A210752 4...15...27...21
%e A210752 5...24...61...86...55
%e A210752 First three polynomials v(n,x): 1, 2 + 3x, 3 + 8x +8x^2
%t A210752 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210752 u[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210752 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210752 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210752 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210752 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210752 TableForm[cu]
%t A210752 Flatten[%]    (* A210751 *)
%t A210752 Table[Expand[v[n, x]], {n, 1, z}]
%t A210752 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210752 TableForm[cv]
%t A210752 Flatten[%]    (* A210752 *)
%Y A210752 Cf. A210751, A208510.
%K A210752 nonn,tabl
%O A210752 1,2
%A A210752 _Clark Kimberling_, Mar 25 2012