A209562 Triangle of coefficients of polynomials v(n,x) jointly generated with A209561; see the Formula section.

1, 2, 1, 3, 2, 1, 4, 4, 3, 1, 5, 7, 7, 4, 1, 6, 11, 14, 11, 5, 1, 7, 16, 25, 25, 16, 6, 1, 8, 22, 41, 50, 41, 22, 7, 1, 9, 29, 63, 91, 91, 63, 29, 8, 1, 10, 37, 92, 154, 182, 154, 92, 37, 9, 1, 11, 46, 129, 246, 336, 336, 246, 129, 46, 10, 1, 12, 56, 175, 375, 582, 672

Offset

1,2

Comments

Alternating row sums: 1,1,2,2,2,2,2,2,2,2,2,2,2,2,...

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

Links

Table of n, a(n) for n=1..72.

Formula

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

v(n,x)=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...1
3...2...1
4...4...3...1
5...7...7...4...1
First three polynomials v(n,x): 1, 3 + x , 5 + 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];
v[n_, x_] := 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[%]   (* A209561 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A209562 *)

Crossrefs

Cf. A209561, A208510.

Sequence in context: A361043 A181847 A366986 * A259344 A239030 A165999

Adjacent sequences: A209559 A209560 A209561 * A209563 A209564 A209565

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 10 2012

Status

approved