A053538 - cp's OEIS frontend

A053538 Triangle: a(n,m) = ways to place p balls in n slots with m in the rightmost p slots, 0<=p<=n, 0<=m<=n, summed over p, a(n,m)= Sum_{k=0..n} binomial(k,m)*binomial(n-k,k-m), (see program line).

n	a(n)
0	1
1	1
2	1
3	2
4	1
5	1
6	3
7	3
8	1
9	1
10	5
11	5
12	4
13	1
14	1
15	8
16	10
17	7
18	5
19	1
20	1
21	13
22	18
23	16
24	9
25	6
26	1
27	1
28	21
29	33
30	31
31	23
32	11
33	7
34	1
35	1
36	34
37	59
38	62
39	47
40	31
41	13
42	8
43	1
44	1
45	55
46	105
47	119
48	101
49	66
50	40
51	15
52	9
53	1
54	1
55	89
56	185
57	227
58	205
59	151
60	88
61	50
62	17
63	10
64	1
65	1
66	144
67	324
68	426
69	414
70	321
71	213
72	113
73	61
74	19
75	11
76	1
77	1

[1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 5, 4, 1, 1, 8, 10, 7, 5, 1, 1, 13, 18, 16, 9, 6, 1, 1, 21, 33, 31, 23, 11, 7, 1, 1, 34, 59, 62, 47, 31, 13, 8, 1, 1, 55, 105, 119, 101, 66, 40, 15, 9, 1, 1, 89, 185, 227, 205, 151, 88, 50, 17, 10, 1, 1, 144, 324, 426, 414, 321, 213, 113, 61, 19, 11, 1, 1]

cp's OEIS Frontend

A053538 Triangle: a(n,m) = ways to place p balls in n slots with m in the rightmost p slots, 0<=p<=n, 0<=m<=n, summed over p, a(n,m)= Sum_{k=0..n} binomial(k,m)*binomial(n-k,k-m), (see program line).

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	2
4	1
5	1
6	3
7	3
8	1
9	1
10	5
11	5
12	4
13	1
14	1
15	8
16	10
17	7
18	5
19	1
20	1
21	13
22	18
23	16
24	9
25	6
26	1
27	1
28	21
29	33
30	31
31	23
32	11
33	7
34	1
35	1
36	34
37	59
38	62
39	47
40	31
41	13
42	8
43	1
44	1
45	55
46	105
47	119
48	101
49	66
50	40
51	15
52	9
53	1
54	1
55	89
56	185
57	227
58	205
59	151
60	88
61	50
62	17
63	10
64	1
65	1
66	144
67	324
68	426
69	414
70	321
71	213
72	113
73	61
74	19
75	11
76	1
77	1

n	a(n)
0	1
1	1
2	1
3	2
4	1
5	1
6	3
7	3
8	1
9	1
10	5
11	5
12	4
13	1
14	1
15	8
16	10
17	7
18	5
19	1
20	1
21	13
22	18
23	16
24	9
25	6
26	1
27	1
28	21
29	33
30	31
31	23
32	11
33	7
34	1
35	1
36	34
37	59
38	62
39	47
40	31
41	13
42	8
43	1
44	1
45	55
46	105
47	119
48	101
49	66
50	40
51	15
52	9
53	1
54	1
55	89
56	185
57	227
58	205
59	151
60	88
61	50
62	17
63	10
64	1
65	1
66	144
67	324
68	426
69	414
70	321
71	213
72	113
73	61
74	19
75	11
76	1
77	1

n	a(n)
0	1
1	1
2	1
3	2
4	1
5	1
6	3
7	3
8	1
9	1
10	5
11	5
12	4
13	1
14	1
15	8
16	10
17	7
18	5
19	1
20	1
21	13
22	18
23	16
24	9
25	6
26	1
27	1
28	21
29	33
30	31
31	23
32	11
33	7
34	1
35	1
36	34
37	59
38	62
39	47
40	31
41	13
42	8
43	1
44	1
45	55
46	105
47	119
48	101
49	66
50	40
51	15
52	9
53	1
54	1
55	89
56	185
57	227
58	205
59	151
60	88
61	50
62	17
63	10
64	1
65	1
66	144
67	324
68	426
69	414
70	321
71	213
72	113
73	61
74	19
75	11
76	1
77	1