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A210864 Triangle of coefficients of polynomials u(n,x) jointly generated with A210865; see the Formula section.

%I A210864 #6 Mar 31 2012 20:30:51
%S A210864 1,2,1,3,3,2,4,9,9,3,5,21,30,21,5,6,41,91,96,47,8,7,71,242,358,278,
%T A210864 101,13,8,113,565,1187,1303,757,209,21,9,169,1182,3517,5238,4364,1951,
%U A210864 422,34,10,241,2263,9332,18816,21213,13674,4802,833,55,11,331
%N A210864 Triangle of coefficients of polynomials u(n,x) jointly generated with A210865; see the Formula section.
%C A210864 Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).
%C A210864 Column 2:  A064999
%C A210864 For a discussion and guide to related arrays, see A208510.
%F A210864 u(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F A210864 v(n,x)=(x+n)*u(n-1,x)+x*v(n-1,x),
%F A210864 where u(1,x)=1, v(1,x)=1.
%e A210864 First five rows:
%e A210864 1
%e A210864 2...1
%e A210864 3...3....2
%e A210864 4...9....9....3
%e A210864 5...21...30...21...5
%e A210864 First three polynomials u(n,x): 1, 2 + x, 3 + 3x + 2x^2.
%t A210864 u[1, x_] := 1; v[1, x_] := 1; z = 14;
%t A210864 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210864 v[n_, x_] := (x + n)*u[n - 1, x] + x*v[n - 1, x];
%t A210864 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210864 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210864 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210864 TableForm[cu]
%t A210864 Flatten[%]   (* A210864 *)
%t A210864 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210864 TableForm[cv]
%t A210864 Flatten[%]   (* A210865 *)
%Y A210864 Cf. A210865, A208510.
%K A210864 nonn,tabl
%O A210864 1,2
%A A210864 _Clark Kimberling_, Mar 28 2012