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%I #5 Mar 31 2012 20:30:51
%S 1,1,2,4,5,3,9,13,13,5,16,37,47,32,8,25,96,152,147,73,13,36,217,469,
%T 587,432,158,21,49,435,1344,2127,2090,1183,330,34,64,793,3487,7186,
%U 8979,6965,3064,669,55,81,1342,8179,22544,35296,35304,21754,7577
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210862; see the Formula section.
%C For n>1, row n starts with (n-1)^2 and ends with F(n+1), where F=A000045 (Fibonacci numbers).
%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 1....2
%e 4....5....3
%e 9....13...13...5
%e 16...37...47...32...8
%e First three polynomials v(n,x): 1, 1 + 2x, 4 + 5x + 3x^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. A210862, A208510.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Mar 28 2012
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