A157181 - cp's OEIS frontend

A157181 A new general triangle sequence based on the Eulerian form in three parts ( subtraction):m=3; 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	5
5	1
6	1
7	17
8	17
9	1
10	1
11	45
12	106
13	45
14	1
15	1
16	105
17	524
18	524
19	105
20	1
21	1
22	229
23	2231
24	4258
25	2231
26	229
27	1
28	1
29	481
30	8547
31	28771
32	28771
33	8547
34	481
35	1
36	1
37	989
38	30424
39	171283
40	290126
41	171283
42	30424
43	989
44	1
45	1
46	2009
47	102926
48	928070
49	2505074
50	2505074
51	928070

[1, 1, 1, 1, 5, 1, 1, 17, 17, 1, 1, 45, 106, 45, 1, 1, 105, 524, 524, 105, 1, 1, 229, 2231, 4258, 2231, 229, 1, 1, 481, 8547, 28771, 28771, 8547, 481, 1, 1, 989, 30424, 171283, 290126, 171283, 30424, 989, 1, 1, 2009, 102926, 928070, 2505074, 2505074, 928070]

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