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A210858 Triangle of coefficients of polynomials u(n,x) jointly generated with A210859; see the Formula section.

%I A210858 #7 Mar 30 2012 18:58:17
%S A210858 1,1,1,1,3,2,1,6,8,3,1,10,24,20,5,1,15,59,82,45,8,1,21,125,271,251,98,
%T A210858 13,1,28,237,765,1073,701,204,21,1,36,413,1898,3860,3802,1842,414,34,
%U A210858 1,45,674,4235,12115,17011,12325,4589,820,55,1,55,1044,8662
%N A210858 Triangle of coefficients of polynomials u(n,x) jointly generated with A210859; see the Formula section.
%C A210858 Row n starts with 1 and ends with F(n), where F=A000045 (Fibonacci numbers).
%C A210858 Alternating row sums:  1,0,0,0,0,0,0,0,...
%C A210858 For a discussion and guide to related arrays, see A208510.
%F A210858 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A210858 v(n,x)=(x+n)*u(n-1,x)+x*v(n-1,x),
%F A210858 where u(1,x)=1, v(1,x)=1.
%e A210858 First five rows:
%e A210858 1
%e A210858 1...1
%e A210858 1...3....2
%e A210858 1...6....8....3
%e A210858 1...10...24...20...5
%e A210858 First three polynomials u(n,x): 1, 1 + x, 1 + 3x + 2x^2.
%t A210858 u[1, x_] := 1; v[1, x_] := 1; z = 14;
%t A210858 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A210858 v[n_, x_] := (x + n)*u[n - 1, x] + x*v[n - 1, x];
%t A210858 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210858 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210858 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210858 TableForm[cu]
%t A210858 Flatten[%]   (* A210858 *)
%t A210858 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210858 TableForm[cv]
%t A210858 Flatten[%]   (* A210859 *)
%Y A210858 Cf. A210806, A208510.
%K A210858 nonn,tabl
%O A210858 1,5
%A A210858 _Clark Kimberling_, Mar 28 2012