A157178 - cp's OEIS frontend

A157178 A new general triangle sequence based on the Eulerian form in three parts:m=2; t0(n,k)=If[nk == 0, 1, Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]] t(n,k,m)=If[n == 0, 1, ( m(n - k) + 1)t0(n - 1 + 1, k - 1) + (mk + 1)t0(n - 1 + 1, k) + mk(n - k)t0(n - 2 + 1, k - 1)].

n	a(n)
0	1
1	1
2	1
3	1
4	8
5	1
6	1
7	21
8	21
9	1
10	1
11	46
12	142
13	46
14	1
15	1
16	95
17	644
18	644
19	95
20	1
21	1
22	192
23	2439
24	5416
25	2439
26	192
27	1
28	1
29	385
30	8415
31	34879
32	34879
33	8415
34	385
35	1
36	1
37	770
38	27556
39	192286
40	358454
41	192286
42	27556
43	770
44	1
45	1
46	1539
47	87486
48	962090
49	3001044
50	3001044
51	962090
52	87486

[1, 1, 1, 1, 8, 1, 1, 21, 21, 1, 1, 46, 142, 46, 1, 1, 95, 644, 644, 95, 1, 1, 192, 2439, 5416, 2439, 192, 1, 1, 385, 8415, 34879, 34879, 8415, 385, 1, 1, 770, 27556, 192286, 358454, 192286, 27556, 770, 1, 1, 1539, 87486, 962090, 3001044, 3001044, 962090, 87486]

cp's OEIS Frontend

A157178 A new general triangle sequence based on the Eulerian form in three parts:m=2; t0(n,k)=If[nk == 0, 1, Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]] t(n,k,m)=If[n == 0, 1, ( m(n - k) + 1)t0(n - 1 + 1, k - 1) + (mk + 1)t0(n - 1 + 1, k) + mk(n - k)t0(n - 2 + 1, k - 1)].

Table of values

List of values

cp's OEIS Frontend

A157178 A new general triangle sequence based on the Eulerian form in three parts:m=2; t0(n,k)=If[n*k == 0, 1, Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]] t(n,k,m)=If[n == 0, 1, ( m*(n - k) + 1)*t0(n - 1 + 1, k - 1) + (m*k + 1)*t0(n - 1 + 1, k) + m*k*(n - k)*t0(n - 2 + 1, k - 1)].

Table of values

List of values

A157178 A new general triangle sequence based on the Eulerian form in three parts:m=2; t0(n,k)=If[nk == 0, 1, Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]] t(n,k,m)=If[n == 0, 1, ( m(n - k) + 1)t0(n - 1 + 1, k - 1) + (mk + 1)t0(n - 1 + 1, k) + mk(n - k)t0(n - 2 + 1, k - 1)].