A207624 Triangle of coefficients of polynomials u(n,x) jointly generated with A102662; see the Formula section.

1, 2, 3, 3, 4, 8, 3, 5, 15, 14, 3, 6, 24, 37, 20, 3, 7, 35, 76, 71, 26, 3, 8, 48, 135, 184, 117, 32, 3, 9, 63, 218, 395, 372, 175, 38, 3, 10, 80, 329, 748, 951, 664, 245, 44, 3, 11, 99, 472, 1295, 2094, 1987, 1084, 327, 50, 3, 12, 120, 651, 2096, 4137, 5032

Offset

1,2

Links

Table of n, a(n) for n=1..62.

Formula

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

where u(1,x)=1, v(1,x)=1. u=A207624; v=A102662.

Example

First five rows:
1
2
3...3
4...8....3
5...15...14...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*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[%]    (* A207624 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A102662 *)

Crossrefs

Cf. A102662.

Sequence in context: A140514 A240209 A047079 * A203990 A238812 A227269

Adjacent sequences: A207621 A207622 A207623 * A207625 A207626 A207627

Keyword

nonn,tabf

Author

Clark Kimberling, Feb 20 2012

Status

approved