A209747 Triangle of coefficients of polynomials u(n,x) jointly generated with A209748; see the Formula section.

1, 1, 2, 3, 4, 2, 5, 10, 6, 2, 9, 20, 18, 8, 2, 15, 40, 44, 28, 10, 2, 25, 76, 102, 80, 40, 12, 2, 41, 142, 222, 210, 130, 54, 14, 2, 67, 260, 466, 512, 380, 196, 70, 16, 2, 109, 470, 948, 1188, 1022, 630, 280, 88, 18, 2, 177, 840, 1884, 2648, 2590, 1848, 980

Offset

1,3

Comments

Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...

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

Links

Table of n, a(n) for n=1..62.

Formula

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

v(n,x)=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
3...4....2
5...10...6....2
9...20...18...8...2
First three polynomials u(n,x): 1, 1 + 2x, 3 + 4x + 2x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, 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[%]    (* A209747 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209748 *)

Crossrefs

Cf. A209748, A208510.

Sequence in context: A293450 A322990 A120636 * A117744 A366481 A361697

Adjacent sequences: A209744 A209745 A209746 * A209748 A209749 A209750

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 13 2012

Status

approved