A209753 Triangle of coefficients of polynomials u(n,x) jointly generated with A209754; see the Formula section.

1, 1, 2, 3, 5, 3, 5, 14, 12, 4, 9, 30, 40, 23, 5, 15, 63, 107, 93, 39, 6, 25, 124, 264, 300, 190, 61, 7, 41, 238, 604, 858, 722, 354, 90, 8, 67, 445, 1319, 2242, 2364, 1559, 615, 127, 9, 109, 818, 2772, 5500, 6966, 5783, 3101, 1011, 173, 10, 177, 1482

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..57.

Formula

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

v(n,x)=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
1...2
3...5....3
5...14...12...4
9...30...40...23...5
First three polynomials u(n,x): 1, 1 + 2x, 3 + 5x + 3x^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] + (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[%]    (* A209753 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209754 *)

Crossrefs

Cf. A209754, A208510.

Sequence in context: A336746 A209769 A114230 * A185191 A103781 A095244

Adjacent sequences: A209750 A209751 A209752 * A209754 A209755 A209756

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 14 2012

Status

approved