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A225094 Number A(n,k) of lattice paths without interior points from {n}^k to {0}^k using steps that decrement one component by 1; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Table of values

n a(n)
0 1
1 1
2 1
3 1
4 1
5 1
6 1
7 2
8 0
9 1
10 1
11 6
12 2
13 0
14 1
15 1
16 24
17 54
18 2
19 0
20 1
21 1
22 120
23 1944
24 384
25 2
26 0
27 1
28 1
29 720
30 99000
31 132000
32 2550
33 2
34 0
35 1
36 1
37 5040
38 6966000
39 79716000
40 8059800
41 16506
42 2
43 0
44 1
45 1
46 40320
47 655678800
48 78928416000
49 57010275000
50 471369024
51 105840
52 2
53 0
54 1

List of values

[1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 6, 2, 0, 1, 1, 24, 54, 2, 0, 1, 1, 120, 1944, 384, 2, 0, 1, 1, 720, 99000, 132000, 2550, 2, 0, 1, 1, 5040, 6966000, 79716000, 8059800, 16506, 2, 0, 1, 1, 40320, 655678800, 78928416000, 57010275000, 471369024, 105840, 2, 0, 1]