A157179 - cp's OEIS frontend

A157179 A new general triangle sequence based on the Eulerian form in three parts ( subtraction):m=1; 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	3
5	1
6	1
7	9
8	9
9	1
10	1
11	23
12	50
13	23
14	1
15	1
16	53
17	236
18	236
19	53
20	1
21	1
22	115
23	983
24	1822
25	983
26	115
27	1
28	1
29	241
30	3723
31	11995
32	11995
33	3723
34	241
35	1
36	1
37	495
38	13168
39	70369
40	117534
41	70369
42	13168
43	495
44	1
45	1
46	1005
47	44382
48	377918
49	997974
50	997974
51	377918
52	44382
53	1005
54	1
55	1

[1, 1, 1, 1, 3, 1, 1, 9, 9, 1, 1, 23, 50, 23, 1, 1, 53, 236, 236, 53, 1, 1, 115, 983, 1822, 983, 115, 1, 1, 241, 3723, 11995, 11995, 3723, 241, 1, 1, 495, 13168, 70369, 117534, 70369, 13168, 495, 1, 1, 1005, 44382, 377918, 997974, 997974, 377918, 44382, 1005, 1, 1]

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