A210225 Triangle of coefficients of polynomials u(n,x) jointly generated with A210226; see the Formula section.

1, 2, 1, 3, 5, 1, 4, 12, 10, 1, 5, 22, 36, 17, 1, 6, 35, 88, 87, 26, 1, 7, 51, 175, 277, 181, 37, 1, 8, 70, 306, 680, 734, 338, 50, 1, 9, 92, 490, 1416, 2196, 1710, 582, 65, 1, 10, 117, 736, 2632, 5402, 6156, 3606, 941, 82, 1, 11, 145, 1053, 4502, 11592

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..60.

Formula

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

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
2...1
3...5....1
4...12...10...1
5...22...36...17...1
First three polynomials u(n,x): 1, 2 + x, 3 + 5x + x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
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[%]     (* A210225 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]     (* A210226 *)

Crossrefs

Cf. A210226, A208510.

Sequence in context: A297582 A134081 A134247 * A180906 A153277 A104029

Adjacent sequences: A210222 A210223 A210224 * A210226 A210227 A210228

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 20 2012

Status

approved