A209583 Triangle of coefficients of polynomials u(n,x) jointly generated with A209584; see the Formula section.

1, 1, 1, 3, 3, 1, 5, 10, 6, 1, 9, 23, 24, 10, 1, 15, 51, 71, 49, 15, 1, 25, 104, 188, 178, 90, 21, 1, 41, 205, 452, 552, 390, 153, 28, 1, 67, 391, 1025, 1530, 1396, 776, 245, 36, 1, 109, 730, 2218, 3927, 4394, 3169, 1435, 374, 45, 1, 177, 1339, 4636, 9502

Offset

1,4

Comments

Alternating row sums: 1,0,1,0,1,0,1,0,1,0,1,0,...

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

Links

Table of n, a(n) for n=1..59.

Formula

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

v(n,x)=(x+1)*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...1
3...3....1
5...10...6....1
9...23...24...10...1
First three polynomials u(n,x): 1, 1 + x, 3 + 3x + 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];
v[n_, x_] := (x + 1)*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[%]   (* A209583 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209584 *)

Crossrefs

Cf. A209584, A208510.

Sequence in context: A208610 A193823 A071945 * A144944 A137426 A269949

Adjacent sequences: A209580 A209581 A209582 * A209584 A209585 A209586

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 11 2012

Status

approved