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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208611 Triangle of coefficients of polynomials v(n,x) jointly generated with A208610; see the Formula section. 3
1, 2, 3, 2, 6, 7, 2, 8, 18, 17, 2, 10, 30, 52, 41, 2, 12, 44, 102, 146, 99, 2, 14, 60, 170, 328, 402, 239, 2, 16, 78, 258, 610, 1014, 1090, 577, 2, 18, 98, 368, 1016, 2076, 3044, 2920, 1393, 2, 20, 120, 502, 1572, 3756, 6792, 8932, 7746, 3363, 2, 22, 144 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

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

v(n,x)=(x+1)*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...3

2...6....7

2...8....18...17

2...10...30...52...41

First five polynomials v(n,x):

1

2 + 3x

2 + 6x + 7x^2

2 + 8x + 18x^2 + 17x^3

2 + 10x + 30x^2 + 52x^3 + 41x^4

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];

v[n_, x_] := (x + 1)*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[%]  (* A208610 *)

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

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

TableForm[cv]

Flatten[%]  (* A208611 *)

CROSSREFS

Cf. A208610.

Sequence in context: A005421 A306156 A276125 * A209582 A158279 A153984

Adjacent sequences:  A208608 A208609 A208610 * A208612 A208613 A208614

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 01 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 14 09:57 EDT 2019. Contains 327995 sequences. (Running on oeis4.)