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

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, 249, 111, 24, 2, 37, 238, 588, 705, 451, 157, 28, 2, 46, 366, 1134, 1749, 1496, 741, 211, 32, 2, 56, 540, 2046, 3927, 4290, 2821, 1135, 273, 36, 2, 67, 770, 3498

Offset

1,2

Links

Table of n, a(n) for n=1..59.

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.

Example

First five rows:
1
2
4...2
7...8...2
11...21...12...2

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 *)

Crossrefs

Cf. A207621.

Sequence in context: A214789 A207631 A207612 * A354766 A207622 A335573

Adjacent sequences: A207617 A207618 A207619 * A207621 A207622 A207623

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 20 2012

Status

approved