cp's OEIS Frontend

A207620 Triangle of coefficients of polynomials u(n,x) jointly generated with A207621; see the Formula section.

%I A207620 #5 Mar 30 2012 18:58:13
%S A207620 1,2,4,2,7,8,2,11,21,12,2,16,45,43,16,2,22,85,119,73,20,2,29,147,280,
%T A207620 249,111,24,2,37,238,588,705,451,157,28,2,46,366,1134,1749,1496,741,
%U A207620 211,32,2,56,540,2046,3927,4290,2821,1135,273,36,2,67,770,3498
%N A207620 Triangle of coefficients of polynomials u(n,x) jointly generated with A207621; see the Formula section.
%F A207620 u(n,x)=u(n-1,x)+v(n-1,x),
%F A207620 v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A207620 where u(1,x)=1, v(1,x)=1.
%e A207620 First five rows:
%e A207620 1
%e A207620 2
%e A207620 4...2
%e A207620 7...8...2
%e A207620 11...21...12...2
%t A207620 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207620 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207620 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
%t A207620 Table[Factor[u[n, x]], {n, 1, z}]
%t A207620 Table[Factor[v[n, x]], {n, 1, z}]
%t A207620 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207620 TableForm[cu]
%t A207620 Flatten[%]    (* A207620 *)
%t A207620 Table[Expand[v[n, x]], {n, 1, z}]
%t A207620 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207620 TableForm[cv]
%t A207620 Flatten[%]    (* A207621 *)
%Y A207620 Cf. A207621.
%K A207620 nonn,tabf
%O A207620 1,2
%A A207620 _Clark Kimberling_, Feb 20 2012