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A207624 Triangle of coefficients of polynomials u(n,x) jointly generated with A102662; see the Formula section.

%I A207624 #5 Mar 30 2012 18:58:13
%S A207624 1,2,3,3,4,8,3,5,15,14,3,6,24,37,20,3,7,35,76,71,26,3,8,48,135,184,
%T A207624 117,32,3,9,63,218,395,372,175,38,3,10,80,329,748,951,664,245,44,3,11,
%U A207624 99,472,1295,2094,1987,1084,327,50,3,12,120,651,2096,4137,5032
%N A207624 Triangle of coefficients of polynomials u(n,x) jointly generated with A102662; see the Formula section.
%F A207624 u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F A207624 where u(1,x)=1, v(1,x)=1.  u=A207624; v=A102662.
%e A207624 First five rows:
%e A207624 1
%e A207624 2
%e A207624 3...3
%e A207624 4...8....3
%e A207624 5...15...14...3
%t A207624 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207624 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207624 v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1
%t A207624 Table[Factor[u[n, x]], {n, 1, z}]
%t A207624 Table[Factor[v[n, x]], {n, 1, z}]
%t A207624 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207624 TableForm[cu]
%t A207624 Flatten[%]    (* A207624 *)
%t A207624 Table[Expand[v[n, x]], {n, 1, z}]
%t A207624 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207624 TableForm[cv]
%t A207624 Flatten[%]    (* A102662 *)
%Y A207624 Cf. A102662.
%K A207624 nonn,tabf
%O A207624 1,2
%A A207624 _Clark Kimberling_, Feb 20 2012