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

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