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

1,2

Links

Table of n, a(n) for n=1..61.

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...2
3...6...2
4...13...10...2
5...24...31...14...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. A207620.

Sequence in context: A248164 A338993 A210222 * A209157 A284785 A076333

Adjacent sequences: A207618 A207619 A207620 * A207622 A207623 A207624

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 20 2012

Status

approved