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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188816 Triangle read by rows: row n gives (coefficients * (n-1)!) in expansion of pieces k=0..n-1 of the probability mass function for the Irwin-Hall distribution, lowest powers first. 0
1, 0, 1, 2, -1, 0, 0, 1, -3, 6, -2, 9, -6, 1, 0, 0, 0, 1, 4, -12, 12, -3, -44, 60, -24, 3, 64, -48, 12, -1, 0, 0, 0, 0, 1, -5, 20, -30, 20, -4, 155, -300, 210, -60, 6, -655, 780, -330, 60, -4, 625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This is the probability distribution for the sum of n independent, random variables, each uniformly distributed on [0,1).

REFERENCES

Hall, Philip. (1927) "The Distribution of Means for Samples of Size N Drawn from a Population in which the Variate Takes Values Between 0 and 1, All Such Values Being Equally Probable". Biometrika, Vol. 19, No. 3/4., pp. 240-245.

LINKS

Table of n, a(n) for n=1..51.

Wikipedia, Irwin-Hall distribution

FORMULA

G.f. for piece k in row n: (1/(n-1)!) * Sum_{j=0..k} (-1)^j * C(n,j) * (x-j)^(n-1).

EXAMPLE

For n = 4, k = 1 (four variables, second piece) the function is the polynomial: 1/6 * (4 - 12x + 12x^2 -3x^3). That gives the subsequence [4, -12, 12, -3].

Triangle begins:

[1];

[0,1], [2,-1];

[0,0,1], [-3,6,-2], [9,-6,1];

CROSSREFS

Differentiation of A188668

Sequence in context: A127840 A145153 A255517 * A168312 A076837 A055363

Adjacent sequences:  A188813 A188814 A188815 * A188817 A188818 A188819

KEYWORD

sign,tabf

AUTHOR

Thomas Dybdahl Ahle, Apr 11 2011

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 8 01:14 EST 2016. Contains 278902 sequences.