A210559 Triangle of coefficients of polynomials u(n,x) jointly generated with A210560; see the Formula section.

1, 1, 2, 1, 4, 3, 1, 6, 8, 5, 1, 8, 15, 17, 8, 1, 10, 24, 38, 33, 13, 1, 12, 35, 70, 86, 63, 21, 1, 14, 48, 115, 180, 187, 117, 34, 1, 16, 63, 175, 330, 437, 390, 214, 55, 1, 18, 80, 252, 553, 882, 1007, 791, 386, 89, 1, 20, 99, 348, 868, 1610, 2219, 2235, 1567

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..64.

Formula

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

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

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

Example

First five rows:
1
1...2
1...4...3
1...6...8....5
1...8...15...17...8
First three polynomials u(n,x): 1, 1 + 2x, 1 + 4x + 3x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%]  (* A210559 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A210560 *)

Crossrefs

Cf. A210560, A208510.

Sequence in context: A197871 A093010 A179000 * A180803 A093966 A103406

Adjacent sequences: A210556 A210557 A210558 * A210560 A210561 A210562

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 22 2012

Status

approved