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%I #5 Mar 30 2012 18:58:17
%S 1,2,1,3,2,2,4,6,7,3,5,15,20,16,5,6,31,57,63,37,8,7,56,153,215,184,81,
%T 13,8,92,370,684,771,513,171,21,9,141,805,2028,2898,2603,1354,351,34,
%U 10,205,1598,5515,10084,11582,8319,3415,703,55,11,286,2940
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210863; see the Formula section.
%C Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).
%C Column 2: A056520
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F v(n,x)=(x+n-1)*u(n-1,x)+x*v(n-1,x),
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2...1
%e 3...2....2
%e 4...6....7....3
%e 5...15...20...16...5
%e First three polynomials u(n,x): 1, 2 + x, 4 + 5x + 2x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 14;
%t u[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
%t v[n_, x_] := (x + n - 1)*u[n - 1, x] + x*v[n - 1, x];
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A210862 *)
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210863 *)
%Y Cf. A210863, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 28 2012
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