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%I #9 Mar 31 2023 03:22:21
%S 1,2,1,3,3,4,7,1,5,14,5,6,25,16,1,7,41,41,7,8,63,91,29,1,9,92,182,92,
%T 9,10,129,336,246,46,1,11,175,582,582,175,11,12,231,957,1254,550,67,1,
%U 13,298,1507,2508,1507,298,13,14,377,2288,4719,3718,1079,92,1
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A207616; see the Formula section.
%F u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=xu(n-1,x)+v(n-1,x)+1, where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2...1
%e 3...3
%e 4...7...1
%e 5...14...5
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t v[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1
%t Table[Factor[u[n, x]], {n, 1, z}]
%t Table[Factor[v[n, x]], {n, 1, z}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A207616 *)
%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[%] (* A207617 *)
%Y Cf. A207616.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Feb 20 2012
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