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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.

Table of values

n a(n)
1 1
2 0
3 1
4 2
5 -1
6 0
7 0
8 1
9 -3
10 6
11 -2
12 9
13 -6
14 1
15 0
16 0
17 0
18 1
19 4
20 -12
21 12
22 -3
23 -44
24 60
25 -24
26 3
27 64
28 -48
29 12
30 -1
31 0
32 0
33 0
34 0
35 1
36 -5
37 20
38 -30
39 20
40 -4
41 155
42 -300
43 210
44 -60
45 6
46 -655
47 780
48 -330
49 60
50 -4
51 625

List of values

[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]