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

1, 2, 2, 3, 8, 4, 20, 4, 5, 40, 24, 6, 70, 84, 8, 7, 112, 224, 64, 8, 168, 504, 288, 16, 9, 240, 1008, 960, 160, 10, 330, 1848, 2640, 880, 32, 11, 440, 3168, 6336, 3520, 384, 12, 572, 5148, 13728, 11440, 2496, 64, 13, 728, 8008, 27456, 32032, 11648

Offset

1,2

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)=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
2...2
3...8
4...20...4
5...40...24
First three polynomials v(n,x): 1, 2 + 2x , 3 + 8x.

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. A210189, A208510.

Sequence in context: A176383 A100551 A267667 * A070267 A205374 A056762

Adjacent sequences: A210187 A210188 A210189 * A210191 A210192 A210193

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 18 2012

Status

approved