login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209160 Triangle of coefficients of polynomials u(n,x) jointly generated with A209161; see the Formula section. 3
1, 2, 1, 3, 6, 4, 4, 13, 20, 10, 5, 22, 52, 62, 28, 6, 33, 104, 192, 192, 76, 7, 46, 180, 444, 680, 584, 208, 8, 61, 284, 870, 1776, 2328, 1760, 568, 9, 78, 420, 1530, 3876, 6768, 7776, 5256, 1552, 10, 97, 592, 2492, 7504, 16260, 24864, 25464, 15584 (list; table; graph; refs; listen; history; text; internal format)
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..54.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

2...1

3...6....4

4...13...20...10

5...22...52...62...28

First three polynomials v(n,x): 1, 2 + x, 3 + 6x + 4x^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] + 2 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[%]    (* A209160 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A209161 *)

CROSSREFS

Cf. A209161, A208510.

Sequence in context: A226122 A133904 A245182 * A257881 A268182 A094339

Adjacent sequences:  A209157 A209158 A209159 * A209161 A209162 A209163

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 08:50 EDT 2019. Contains 328056 sequences. (Running on oeis4.)