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A207625 Triangle of coefficients of polynomials u(n,x) jointly generated with A207626; see the Formula section.

%I A207625 #5 Mar 30 2012 18:58:13
%S A207625 1,2,4,3,7,12,3,11,32,21,3,16,70,83,30,3,22,135,247,161,39,3,29,238,
%T A207625 616,622,266,48,3,37,392,1358,1946,1276,398,57,3,46,612,2730,5244,
%U A207625 4854,2290,557,66,3,56,915,5106,12630,15622,10312,3745,743,75,3,67
%N A207625 Triangle of coefficients of polynomials u(n,x) jointly generated with A207626; see the Formula section.
%F A207625 u(n,x)=u(n-1,x)+v(n-1,x),
%F A207625 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A207625 where u(1,x)=1, v(1,x)=1.
%e A207625 First five rows:
%e A207625 1
%e A207625 2
%e A207625 4....3
%e A207625 7....12...3
%e A207625 11...32...21...3
%t A207625 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207625 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207625 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
%t A207625 Table[Factor[u[n, x]], {n, 1, z}]
%t A207625 Table[Factor[v[n, x]], {n, 1, z}]
%t A207625 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207625 TableForm[cu]
%t A207625 Flatten[%]    (* A207625 *)
%t A207625 Table[Expand[v[n, x]], {n, 1, z}]
%t A207625 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207625 TableForm[cv]
%t A207625 Flatten[%]    (* A207626 *)
%Y A207625 Cf. A207626.
%K A207625 nonn,tabf
%O A207625 1,2
%A A207625 _Clark Kimberling_, Feb 21 2012