cp's OEIS Frontend

A207631 Triangle of coefficients of polynomials u(n,x) jointly generated with A207632; see the Formula section.

%I A207631 #5 Mar 30 2012 18:58:13
%S A207631 1,2,4,2,7,6,2,12,15,8,2,20,33,25,10,2,33,68,66,37,12,2,54,134,159,
%T A207631 113,51,14,2,88,256,359,309,176,67,16,2,143,478,774,781,536,257,85,18,
%U A207631 2,232,877,1611,1864,1493,860,358,105,20,2,376,1587,3262,4256
%N A207631 Triangle of coefficients of polynomials u(n,x) jointly generated with A207632; see the Formula section.
%F A207631 u(n,x)=u(n-1,x)+v(n-1,x),
%F A207631 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A207631 where u(1,x)=1, v(1,x)=1.
%e A207631 First five rows:
%e A207631 1
%e A207631 2
%e A207631 4...2
%e A207631 7...6...2
%e A207631 12...15...8...2
%t A207631 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207631 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207631 v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1
%t A207631 Table[Factor[u[n, x]], {n, 1, z}]
%t A207631 Table[Factor[v[n, x]], {n, 1, z}]
%t A207631 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207631 TableForm[cu]
%t A207631 Flatten[%]  (* A207631 *)
%t A207631 Table[Expand[v[n, x]], {n, 1, z}]
%t A207631 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207631 TableForm[cv]
%t A207631 Flatten[%]  (* A207632 *)
%Y A207631 Cf. A207632.
%K A207631 nonn,tabf
%O A207631 1,2
%A A207631 _Clark Kimberling_, Feb 23 2012