login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144398 Coefficients of a symmetrical polynomial set:( Pascal's triangle with central zeros) p(x,n)=If[n <= 4, Sum[Binomial[n, i]*x^i, {i, 0, n}], x^n + n*x^(n - 1) + Binomial[n, 2]*x^(n - 2) + n*x + Binomial[n, 2]*x^2 + 1]. 0
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 0, 15, 6, 1, 1, 7, 21, 0, 0, 21, 7, 1, 1, 8, 28, 0, 0, 0, 28, 8, 1, 1, 9, 36, 0, 0, 0, 0, 36, 9, 1, 1, 10, 45, 0, 0, 0, 0, 0, 45, 10, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are: (related to A014206)

{1, 2, 4, 8, 16, 32, 44, 58, 74, 92, 112}

LINKS

Table of n, a(n) for n=1..66.

FORMULA

p(x,n)=If[n <= 4, Sum[Binomial[n, i]*x^i, {i, 0, n}], x^n + n*x^(n - 1) + Binomial[n, 2]*x^(n - 2) + n*x + Binomial[n, 2]*x^2 + 1]; t(n,m)=coefficients(p(x,n)).

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 3, 3, 1},

{1, 4, 6, 4, 1},

{1, 5, 10, 10, 5, 1},

{1, 6, 15, 0, 15, 6, 1},

{1, 7, 21, 0, 0, 21, 7, 1},

{1, 8, 28, 0, 0, 0, 28, 8, 1},

{1, 9, 36, 0, 0, 0, 0, 36, 9, 1},

{1, 10, 45, 0, 0, 0, 0, 0, 45, 10, 1}

MATHEMATICA

Clear[p, n]; p[x_, n_] = If[n <= 4, Sum[Binomial[n, i]*x^i, {i, 0, n}], x^n + n*x^(n - 1) + Binomial[n, 2]*x^(n - 2) + n*x + Binomial[n, 2]*x^2 + 1]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]

CROSSREFS

Sequence in context: A275198 A095145 A095144 * A034932 A180183 A273914

Adjacent sequences:  A144395 A144396 A144397 * A144399 A144400 A144401

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 03 2008

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 June 4 05:19 EDT 2020. Contains 334815 sequences. (Running on oeis4.)