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

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, 22, 2, 8, 91, 308, 456, 340, 133, 26, 2, 9, 128, 546, 1044, 1045, 584, 183, 30, 2, 10, 174, 912, 2178, 2794, 2080, 924, 241, 34, 2, 11, 230, 1452, 4224, 6721, 6370

Offset: 1

Author

Clark Kimberling, Feb 20 2012

Keywords

• nonn
• tabl

Examples

			First five rows:
1
2...2
3...6...2
4...13...10...2
5...24...31...14...2
		

Crossrefs

Cf. A207620.

Programs

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
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
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A207620 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207621 *)

Formula

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.