A210189 Triangle of coefficients of polynomials u(n,x) jointly generated with A210190; see the Formula section.

1, 3, 6, 2, 10, 10, 15, 30, 4, 21, 70, 28, 28, 140, 112, 8, 36, 252, 336, 72, 45, 420, 840, 360, 16, 55, 660, 1848, 1320, 176, 66, 990, 3696, 3960, 1056, 32, 78, 1430, 6864, 10296, 4576, 416, 91, 2002, 12012, 24024, 16016, 2912, 64, 105, 2730, 20020

Offset

1,2

Comments

Column 1: triangular numbers: A000217

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

Links

Table of n, a(n) for n=1..52.

Formula

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

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

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

Example

First five rows:
1
3
6....2
10...10
15...30...4
First three polynomials u(n,x): 1, 3, 6 + 2x.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 x*u[n - 1, 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[%]   (* A210189 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210190 *)

Crossrefs

Cf. A210190, A208510.

Sequence in context: A354087 A210187 A364365 * A257506 A210035 A210199

Adjacent sequences: A210186 A210187 A210188 * A210190 A210191 A210192

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 18 2012

Status

approved