A207626 Triangle of coefficients of polynomials v(n,x) jointly generated with A207625; see the Formula section.

1, 2, 3, 3, 9, 3, 4, 20, 18, 3, 5, 38, 62, 27, 3, 6, 65, 164, 131, 36, 3, 7, 103, 369, 461, 227, 45, 3, 8, 154, 742, 1324, 1010, 350, 54, 3, 9, 220, 1372, 3298, 3578, 1892, 500, 63, 3, 10, 303, 2376, 7386, 10768, 8022, 3188, 677, 72, 3, 11, 405, 3903, 15222

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)=2x*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...3
3...9...3
4...20...18...3
5...38...62...27...3

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_] := 2 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[%]    (* A207625 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207626 *)

Crossrefs

Cf. A207625.

Sequence in context: A267563 A166994 A059083 * A232324 A124931 A210226

Adjacent sequences: A207623 A207624 A207625 * A207627 A207628 A207629

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 21 2012

Status

approved