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A207617 Triangle of coefficients of polynomials v(n,x) jointly generated with A207616; see the Formula section.

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