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%I #5 Mar 30 2012 18:58:17
%S 1,3,1,6,7,1,11,21,15,1,19,53,60,31,1,32,118,191,155,63,1,53,246,514,
%T 593,378,127,1,87,489,1261,1863,1683,889,255,1,142,941,2890,5233,6029,
%U 4501,2040,511,1,231,1767,6311,13527,19026,18068,11543,4599
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210750; see the Formula section.
%C Row n starts with -2+F(n+3) and ends with 1, where F=A000045 (Fibonacci numbers).
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 3....1
%e 6....7....1
%e 11...21...15...1
%e 19...53...60...31...1
%e First three polynomials u(n,x): 1, 3+ x, 6 + 7x + x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%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[%] (* A210749 *)
%t Table[Expand[v[n, x]], {n, 1, z}]
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210750 *)
%Y Cf. A210750, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 25 2012