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A054651 Triangle T(n,k) read by rows giving coefficients in expansion of n! * Sum_{i=0..n} C(x,i) in descending powers of x.

Table of values

n a(n)
0 1
1 1
2 1
3 1
4 1
5 2
6 1
7 0
8 5
9 6
10 1
11 -2
12 11
13 14
14 24
15 1
16 -5
17 25
18 5
19 94
20 120
21 1
22 -9
23 55
24 -75
25 304
26 444
27 720
28 1
29 -14
30 112
31 -350
32 1099
33 364
34 3828
35 5040
36 1
37 -20
38 210
39 -1064
40 3969
41 -4340
42 15980
43 25584
44 40320
45 1
46 -27
47 366
48 -2646
49 12873
50 -31563
51 79064
52 34236
53 270576
54 362880

List of values

[1, 1, 1, 1, 1, 2, 1, 0, 5, 6, 1, -2, 11, 14, 24, 1, -5, 25, 5, 94, 120, 1, -9, 55, -75, 304, 444, 720, 1, -14, 112, -350, 1099, 364, 3828, 5040, 1, -20, 210, -1064, 3969, -4340, 15980, 25584, 40320, 1, -27, 366, -2646, 12873, -31563, 79064, 34236, 270576, 362880]