A209568 Triangle of coefficients of polynomials v(n,x) jointly generated with A209567; see the Formula section.

1, 2, 2, 3, 5, 3, 4, 10, 11, 4, 5, 17, 28, 21, 5, 6, 26, 58, 67, 36, 6, 7, 37, 105, 166, 142, 57, 7, 8, 50, 173, 350, 416, 274, 85, 8, 9, 65, 266, 659, 1011, 940, 491, 121, 9, 10, 82, 388, 1141, 2156, 2612, 1955, 829, 166, 10, 11, 101, 543, 1852, 4172, 6265

Offset

1,2

Comments

Row n begins and ends with n.

Column 2: (n-1)^2, for n>1.

Alternating row sums: 1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,...

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

Links

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

Formula

u(n,x)=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...5...3
4...10...11...4
5...17...28...21...5
First three polynomials v(n,x): 1, 2+2x, 3+5x+3x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 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[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[%]   (* A209567 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209568 *)

Crossrefs

Cf. A209567, A208510.

Sequence in context: A210232 A047666 A285935 * A227641 A295097 A295551

Adjacent sequences: A209565 A209566 A209567 * A209569 A209570 A209571

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved