A207618 Triangle of coefficients of polynomials u(n,x) jointly generated with A207619; see the Formula section.

1, 2, 3, 3, 4, 7, 6, 5, 12, 17, 12, 6, 18, 34, 40, 24, 7, 25, 58, 91, 92, 48, 8, 33, 90, 173, 234, 208, 96, 9, 42, 131, 295, 489, 584, 464, 192, 10, 52, 182, 467, 906, 1328, 1424, 1024, 384, 11, 63, 244, 700, 1545, 2651, 3496, 3408, 2240, 768, 12, 75, 318

Offset: 1

Author

Clark Kimberling, Feb 20 2012

Keywords

• nonn
• tabf

Examples

			First five rows:
1
2
3...3
4...7....6
5...12...17...12
		

Crossrefs

Cf. A207619.

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] + 2 x*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[%]    (* A207618 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207619 *)

Formula

u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.