A209767 Triangle of coefficients of polynomials u(n,x) jointly generated with A209768; see the Formula section.

1, 1, 2, 2, 6, 5, 3, 12, 20, 12, 4, 21, 52, 63, 29, 5, 33, 109, 199, 187, 70, 6, 48, 200, 490, 700, 536, 169, 7, 66, 334, 1032, 1988, 2322, 1498, 408, 8, 87, 520, 1948, 4742, 7488, 7378, 4109, 985, 9, 111, 767, 3388, 10004, 19992, 26664, 22685, 11109

Offset

1,3

Comments

For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..54.

Formula

u(n,x)=x*u(n-1,x)+(x+1)*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
1...2
2...6....5
3...12...20...12
4...21...52...63...29
First three polynomials u(n,x): 1, 1 + 2x, 2 + 6x + 5x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A209767 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209768 *)

Crossrefs

Cf. A209768, A208510.

Sequence in context: A064766 A019749 A209773 * A122070 A181661 A144160

Adjacent sequences: A209764 A209765 A209766 * A209768 A209769 A209770

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 15 2012

Status

approved