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

%I A210865 #6 Mar 31 2012 20:30:51
%S A210865 1,2,2,6,7,3,12,21,18,5,20,61,75,42,8,30,151,262,231,93,13,42,323,829,
%T A210865 1025,656,196,21,56,617,2330,3935,3607,1742,401,34,72,1081,5815,13578,
%U A210865 16849,11723,4380,799,55,90,1771,13070,42167,69475,65727
%N A210865 Triangle of coefficients of polynomials v(n,x) jointly generated with A210864; see the Formula section.
%C A210865 For n>1, row n starts with n(n-1) and ends with F(n+1), where F=A000045 (Fibonacci numbers).
%C A210865 For a discussion and guide to related arrays, see A208510.
%F A210865 u(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F A210865 v(n,x)=(x+n)*u(n-1,x)+x*v(n-1,x),
%F A210865 where u(1,x)=1, v(1,x)=1.
%e A210865 First five rows:
%e A210865 1
%e A210865 2....2
%e A210865 6....7....3
%e A210865 12...21...18...5
%e A210865 20...61...75...34...8
%e A210865 First three polynomials v(n,x): 1, 2 + 2x, 6 + 7x + 3x^2
%t A210865 u[1, x_] := 1; v[1, x_] := 1; z = 14;
%t A210865 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210865 v[n_, x_] := (x + n)*u[n - 1, x] + x*v[n - 1, x];
%t A210865 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210865 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210865 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210865 TableForm[cu]
%t A210865 Flatten[%]   (* A210864 *)
%t A210865 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210865 TableForm[cv]
%t A210865 Flatten[%]   (* A210865 *)
%Y A210865 Cf. A210864, A208510.
%K A210865 nonn,tabl
%O A210865 1,2
%A A210865 _Clark Kimberling_, Mar 28 2012