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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143596 A symmetrical triangle sequence of coefficients of a difference polynomial' p(x,n)=((x + 1)^(2*n) - (x^2 + 1)^n)/(2*x). 1
1, 2, 2, 2, 3, 6, 10, 6, 3, 4, 12, 28, 32, 28, 12, 4, 5, 20, 60, 100, 126, 100, 60, 20, 5, 6, 30, 110, 240, 396, 452, 396, 240, 110, 30, 6, 7, 42, 182, 490, 1001, 1484, 1716, 1484, 1001, 490, 182, 42, 7, 8, 56, 280, 896, 2184, 3976, 5720, 6400, 5720, 3976, 2184, 896, 280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums are:{1, 6, 28, 120, 496, 2016, 8128, 32640, 130816, 523776}.

LINKS

Table of n, a(n) for n=1..62.

FORMULA

p(x,n)=((x + 1)^(2*n) - (x^2 + 1)^n)/(2*x); t(n,m)=coefficients(t(n,m)).

EXAMPLE

{1},

{2, 2, 2},

{3, 6, 10, 6, 3},

{4, 12, 28, 32, 28, 12, 4},

{5, 20, 60, 100, 126, 100, 60, 20, 5},

{6, 30, 110, 240, 396, 452, 396, 240, 110, 30, 6},

{7, 42, 182, 490, 1001, 1484, 1716, 1484, 1001, 490, 182, 42, 7},

{8, 56, 280, 896, 2184, 3976, 5720, 6400, 5720, 3976, 2184, 896, 280, 56, 8},

{9, 72, 408, 1512, 4284, 9240, 15912, 21816, 24310, 21816, 15912, 9240, 4284, 1512, 408, 72, 9},

{10, 90, 570, 2400, 7752, 19320, 38760, 62880, 83980, 92252, 83980, 62880, 38760, 19320, 7752, 2400, 570, 90, 10}

MATHEMATICA

Clear[p, x, n, m]; p[x_, n_] = ((x + 1)^(2*n) - (x^2 + 1)^n)/(2*x); Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}]; Flatten[%]

CROSSREFS

Sequence in context: A147851 A321380 A218694 * A091712 A125721 A049798

Adjacent sequences:  A143593 A143594 A143595 * A143597 A143598 A143599

KEYWORD

nonn,tabf

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 25 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 August 26 00:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)