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A210749 Triangle of coefficients of polynomials u(n,x) jointly generated with A210750; see the Formula section.

%I A210749 #5 Mar 30 2012 18:58:17
%S A210749 1,3,1,6,7,1,11,21,15,1,19,53,60,31,1,32,118,191,155,63,1,53,246,514,
%T A210749 593,378,127,1,87,489,1261,1863,1683,889,255,1,142,941,2890,5233,6029,
%U A210749 4501,2040,511,1,231,1767,6311,13527,19026,18068,11543,4599
%N A210749 Triangle of coefficients of polynomials u(n,x) jointly generated with A210750; see the Formula section.
%C A210749 Row n starts with -2+F(n+3) and ends with 1, where F=A000045 (Fibonacci numbers).
%C A210749 For a discussion and guide to related arrays, see A208510.
%F A210749 u(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A210749 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A210749 where u(1,x)=1, v(1,x)=1.
%e A210749 First five rows:
%e A210749 1
%e A210749 3....1
%e A210749 6....7....1
%e A210749 11...21...15...1
%e A210749 19...53...60...31...1
%e A210749 First three polynomials u(n,x): 1, 3+ x, 6 + 7x + x^2.
%t A210749 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210749 u[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A210749 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210749 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210749 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210749 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210749 TableForm[cu]
%t A210749 Flatten[%]    (* A210749 *)
%t A210749 Table[Expand[v[n, x]], {n, 1, z}]
%t A210749 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210749 TableForm[cv]
%t A210749 Flatten[%]    (* A210750 *)
%Y A210749 Cf. A210750, A208510.
%K A210749 nonn,tabl
%O A210749 1,2
%A A210749 _Clark Kimberling_, Mar 25 2012