

A188816


Triangle read by rows: row n gives (coefficients * (n1)!) in expansion of pieces k=0..n1 of the probability mass function for the IrwinHall 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
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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. 240245.


LINKS

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


FORMULA

G.f. for piece k in row n: (1/(n1)!) * Sum_{j=0..k} (1)^j * C(n,j) * (xj)^(n1).


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



