A209582 Triangle of coefficients of polynomials v(n,x) jointly generated with A209581; see the Formula section.

1, 2, 3, 2, 6, 7, 3, 10, 17, 15, 3, 16, 39, 46, 31, 4, 21, 69, 129, 119, 63, 4, 30, 112, 260, 386, 296, 127, 5, 36, 172, 492, 890, 1082, 713, 255, 5, 48, 242, 828, 1898, 2832, 2897, 1674, 511, 6, 55, 342, 1318, 3522, 6682, 8511, 7495, 3851, 1023, 6, 70

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..57.

Formula

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

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

where u(1,x)=1, v(1,x)=1.

Example

First five rows:
1
2...3
2...6....7
3...10...17...15
3...16...39...46...31
First three polynomials v(n,x): 1, 2 + 3x , 2 + 6x + 7x^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 + 1)*u[n - 1, x] + 2 x*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[%]   (* A209581 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209582 *)

Crossrefs

Cf. A209581, A208510.

Sequence in context: A306156 A276125 A208611 * A158279 A153984 A025502

Adjacent sequences: A209579 A209580 A209581 * A209583 A209584 A209585

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 11 2012

Status

approved