%I #9 Mar 31 2023 03:22:53

%S 1,2,2,3,6,2,4,13,10,2,5,24,31,14,2,6,40,76,57,18,2,7,62,161,176,91,

%T 22,2,8,91,308,456,340,133,26,2,9,128,546,1044,1045,584,183,30,2,10,

%U 174,912,2178,2794,2080,924,241,34,2,11,230,1452,4224,6721,6370

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A207620; see the Formula section.

%F u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 2...2

%e 3...6...2

%e 4...13...10...2

%e 5...24...31...14...2

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := u[n - 1, x] + v[n - 1, x]

%t v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1

%t Table[Factor[u[n, x]], {n, 1, z}]

%t Table[Factor[v[n, x]], {n, 1, z}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%] (* A207620 *)

%t Table[Expand[v[n, x]], {n, 1, z}]

%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

%t TableForm[cv]

%t Flatten[%] (* A207621 *)

%Y Cf. A207620.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Feb 20 2012