A209158 Triangle of coefficients of polynomials u(n,x) jointly generated with A209159; see the Formula section.

1, 2, 1, 3, 5, 3, 4, 11, 13, 5, 5, 19, 35, 31, 11, 6, 29, 73, 101, 73, 21, 7, 41, 131, 247, 275, 167, 43, 8, 55, 213, 509, 769, 717, 377, 85, 9, 71, 323, 935, 1787, 2255, 1811, 839, 171, 10, 89, 465, 1581, 3657, 5829, 6321, 4461, 1849, 341, 11, 109, 643

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..58.

Formula

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

v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,

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

Example

First five rows:
1
2...1
3...5....5
4...11...13...5
5...19...35...31...11
First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 5x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + 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[%]    (* A209158 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A209159 *)

Crossrefs

Cf. A209159, A208510.

Sequence in context: A069931 A373534 A209152 * A209135 A258236 A258244

Adjacent sequences: A209155 A209156 A209157 * A209159 A209160 A209161

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 07 2012

Status

approved