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A207614 Triangle of coefficients of polynomials u(n,x) jointly generated with A207615; see the Formula section.

%I A207614 #5 Mar 30 2012 18:58:13
%S A207614 1,2,5,1,11,5,1,23,16,6,1,47,44,23,7,1,95,112,74,31,8,1,191,272,216,
%T A207614 113,40,9,1,383,640,592,368,162,50,10,1,767,1472,1552,1112,579,222,61,
%U A207614 11,1,1535,3328,3936,3184,1902,861,294,73,12,1,3071,7424,9728
%N A207614 Triangle of coefficients of polynomials u(n,x) jointly generated with A207615; see the Formula section.
%F A207614 u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=u(n-1,x)+(x+1)v(n-1,x)+1,
%F A207614 where u(1,x)=1, v(1,x)=1.
%e A207614 First five rows:
%e A207614 1
%e A207614 2
%e A207614 5....1
%e A207614 11...5....1
%e A207614 23...16...6...1
%t A207614 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207614 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207614 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
%t A207614 Table[Factor[u[n, x]], {n, 1, z}]
%t A207614 Table[Factor[v[n, x]], {n, 1, z}]
%t A207614 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207614 TableForm[cu]
%t A207614 Flatten[%]    (* A207614 *)
%t A207614 Table[Expand[v[n, x]], {n, 1, z}]
%t A207614 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207614 TableForm[cv]
%t A207614 Flatten[%]    (* A207615 *)
%Y A207614 Cf. A207615.
%K A207614 nonn,tabf
%O A207614 1,2
%A A207614 _Clark Kimberling_, Feb 20 2012