A055216 - cp's OEIS frontend

A055216 Triangle T(n,k) by rows, n >= 0, 0<=k<=n: T(n,k) = Sum_{i=0..n-k} binomial(n-k,i) *Sum_{j=0..k-i} binomial(i,j).

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	3
8	3
9	1
10	1
11	4
12	6
13	3
14	1
15	1
16	5
17	10
18	8
19	3
20	1
21	1
22	6
23	15
24	17
25	9
26	3
27	1
28	1
29	7
30	21
31	31
32	23
33	9
34	3
35	1
36	1
37	8
38	28
39	51
40	50
41	26
42	9
43	3
44	1
45	1
46	9
47	36
48	78
49	96
50	66
51	27
52	9
53	3
54	1
55	1
56	10
57	45
58	113
59	168
60	147
61	76
62	27
63	9
64	3
65	1
66	1
67	11
68	55
69	157
70	274
71	294
72	192
73	80
74	27
75	9
76	3
77	1

[1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 3, 1, 1, 5, 10, 8, 3, 1, 1, 6, 15, 17, 9, 3, 1, 1, 7, 21, 31, 23, 9, 3, 1, 1, 8, 28, 51, 50, 26, 9, 3, 1, 1, 9, 36, 78, 96, 66, 27, 9, 3, 1, 1, 10, 45, 113, 168, 147, 76, 27, 9, 3, 1, 1, 11, 55, 157, 274, 294, 192, 80, 27, 9, 3, 1]

cp's OEIS Frontend

A055216 Triangle T(n,k) by rows, n >= 0, 0<=k<=n: T(n,k) = Sum_{i=0..n-k} binomial(n-k,i) *Sum_{j=0..k-i} binomial(i,j).

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	3
8	3
9	1
10	1
11	4
12	6
13	3
14	1
15	1
16	5
17	10
18	8
19	3
20	1
21	1
22	6
23	15
24	17
25	9
26	3
27	1
28	1
29	7
30	21
31	31
32	23
33	9
34	3
35	1
36	1
37	8
38	28
39	51
40	50
41	26
42	9
43	3
44	1
45	1
46	9
47	36
48	78
49	96
50	66
51	27
52	9
53	3
54	1
55	1
56	10
57	45
58	113
59	168
60	147
61	76
62	27
63	9
64	3
65	1
66	1
67	11
68	55
69	157
70	274
71	294
72	192
73	80
74	27
75	9
76	3
77	1

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	3
8	3
9	1
10	1
11	4
12	6
13	3
14	1
15	1
16	5
17	10
18	8
19	3
20	1
21	1
22	6
23	15
24	17
25	9
26	3
27	1
28	1
29	7
30	21
31	31
32	23
33	9
34	3
35	1
36	1
37	8
38	28
39	51
40	50
41	26
42	9
43	3
44	1
45	1
46	9
47	36
48	78
49	96
50	66
51	27
52	9
53	3
54	1
55	1
56	10
57	45
58	113
59	168
60	147
61	76
62	27
63	9
64	3
65	1
66	1
67	11
68	55
69	157
70	274
71	294
72	192
73	80
74	27
75	9
76	3
77	1

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	3
8	3
9	1
10	1
11	4
12	6
13	3
14	1
15	1
16	5
17	10
18	8
19	3
20	1
21	1
22	6
23	15
24	17
25	9
26	3
27	1
28	1
29	7
30	21
31	31
32	23
33	9
34	3
35	1
36	1
37	8
38	28
39	51
40	50
41	26
42	9
43	3
44	1
45	1
46	9
47	36
48	78
49	96
50	66
51	27
52	9
53	3
54	1
55	1
56	10
57	45
58	113
59	168
60	147
61	76
62	27
63	9
64	3
65	1
66	1
67	11
68	55
69	157
70	274
71	294
72	192
73	80
74	27
75	9
76	3
77	1