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

%I A210751 #5 Mar 30 2012 18:58:17
%S A210751 1,2,2,3,6,5,4,12,19,13,5,20,46,59,34,6,30,90,166,179,89,7,42,155,370,
%T A210751 572,533,233,8,56,245,715,1426,1904,1564,610,9,72,364,1253,3046,5240,
%U A210751 6171,4536,1597,10,90,516,2044,5845,12237,18561,19581,13031
%N A210751 Triangle of coefficients of polynomials u(n,x) jointly generated with A210752; see the Formula section.
%C A210751 Row n starts with n and ends with F(2n-1), where F=A000045 (Fibonacci numbers).
%C A210751 For a discussion and guide to related arrays, see A208510.
%F A210751 u(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A210751 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A210751 where u(1,x)=1, v(1,x)=1.
%e A210751 First five rows:
%e A210751 1
%e A210751 2...2
%e A210751 3...6....5
%e A210751 4...12...19...13
%e A210751 5...20...46...59...34
%e A210751 First three polynomials u(n,x): 1, 2 + 2x, 3 + 6x + 5x^2.
%t A210751 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210751 u[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210751 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210751 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210751 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210751 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210751 TableForm[cu]
%t A210751 Flatten[%]    (* A210751 *)
%t A210751 Table[Expand[v[n, x]], {n, 1, z}]
%t A210751 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210751 TableForm[cv]
%t A210751 Flatten[%]    (* A210752 *)
%Y A210751 Cf. A210752, A208510.
%K A210751 nonn,tabl
%O A210751 1,2
%A A210751 _Clark Kimberling_, Mar 25 2012