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%I #5 Mar 30 2012 18:58:17
%S 1,2,2,3,6,3,4,16,17,5,5,35,62,40,8,6,66,189,206,90,13,7,112,494,822,
%T 603,191,21,8,176,1133,2787,3101,1638,393,34,9,261,2337,8255,13209,
%U 10483,4175,786,55,10,370,4427,21730,48753,55089,32705,10157,1540
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210858; see the Formula section.
%C Row n starts with 1 and ends with F(n+1), where F=A000045 (Fibonacci numbers).
%C Alternating row sums: 1,0,0,0,0,0,0,0,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+x*v(n-1,x),
%F v(n,x)=(x+n)*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...2
%e 3...6....3
%e 4...16...17...5
%e 5...35...62...40...8
%e First three polynomials v(n,x): 1, 2 + 2x, 3 + 6x + 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];
%t v[n_, x_] := (x + n)*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[%] (* A210858 *)
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210859 *)
%t Table[u[n, x] /. x -> 1, {n, 1, z}]
%t Table[v[n, x] /. x -> 1, {n, 1, z}]
%t Table[u[n, x] /. x -> -1, {n, 1, z}]
%t Table[v[n, x] /. x -> -1, {n, 1, z}]
%Y Cf. A210858, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 28 2012
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