A157180 - cp's OEIS frontend

A157180 A new general triangle sequence based on the Eulerian form in three parts ( subtraction):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	4
5	1
6	1
7	13
8	13
9	1
10	1
11	34
12	78
13	34
14	1
15	1
16	79
17	380
18	380
19	79
20	1
21	1
22	172
23	1607
24	3040
25	1607
26	172
27	1
28	1
29	361
30	6135
31	20383
32	20383
33	6135
34	361
35	1
36	1
37	742
38	21796
39	120826
40	203830
41	120826
42	21796
43	742
44	1
45	1
46	1507
47	73654
48	652994
49	1751524
50	1751524
51	652994
52	73654

[1, 1, 1, 1, 4, 1, 1, 13, 13, 1, 1, 34, 78, 34, 1, 1, 79, 380, 380, 79, 1, 1, 172, 1607, 3040, 1607, 172, 1, 1, 361, 6135, 20383, 20383, 6135, 361, 1, 1, 742, 21796, 120826, 203830, 120826, 21796, 742, 1, 1, 1507, 73654, 652994, 1751524, 1751524, 652994, 73654]

cp's OEIS Frontend

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List of values