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A210863 Triangle of coefficients of polynomials v(n,x) jointly generated with A210862; see the Formula section.

%I A210863 #5 Mar 31 2012 20:30:51
%S A210863 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 A210863 587,432,158,21,49,435,1344,2127,2090,1183,330,34,64,793,3487,7186,
%U A210863 8979,6965,3064,669,55,81,1342,8179,22544,35296,35304,21754,7577
%N A210863 Triangle of coefficients of polynomials v(n,x) jointly generated with A210862; see the Formula section.
%C A210863 For n>1, row n starts with (n-1)^2 and ends with F(n+1), where F=A000045 (Fibonacci numbers).
%C A210863 For a discussion and guide to related arrays, see A208510.
%F A210863 u(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F A210863 v(n,x)=(x+n-1)*u(n-1,x)+x*v(n-1,x),
%F A210863 where u(1,x)=1, v(1,x)=1.
%e A210863 First five rows:
%e A210863 1
%e A210863 1....2
%e A210863 4....5....3
%e A210863 9....13...13...5
%e A210863 16...37...47...32...8
%e A210863 First three polynomials v(n,x): 1, 1 + 2x, 4 + 5x + 3x^2
%t A210863 u[1, x_] := 1; v[1, x_] := 1; z = 14;
%t A210863 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210863 v[n_, x_] := (x + n - 1)*u[n - 1, x] + x*v[n - 1, x];
%t A210863 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210863 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210863 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210863 TableForm[cu]
%t A210863 Flatten[%]   (* A210862 *)
%t A210863 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210863 TableForm[cv]
%t A210863 Flatten[%]   (* A210863 *)
%Y A210863 Cf. A210862, A208510.
%K A210863 nonn,tabl
%O A210863 1,3
%A A210863 _Clark Kimberling_, Mar 28 2012