A157177 - cp's OEIS frontend

A157177 A new general triangle sequence based on the Eulerian form in three parts: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	5
5	1
6	1
7	13
8	13
9	1
10	1
11	29
12	82
13	29
14	1
15	1
16	61
17	368
18	368
19	61
20	1
21	1
22	125
23	1399
24	3010
25	1399
26	125
27	1
28	1
29	253
30	4863
31	19243
32	19243
33	4863
34	253
35	1
36	1
37	509
38	16048
39	106099
40	194846
41	106099
42	16048
43	509
44	1
45	1
46	1021
47	51298
48	532466
49	1622734
50	1622734
51	532466
52	51298

[1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 29, 82, 29, 1, 1, 61, 368, 368, 61, 1, 1, 125, 1399, 3010, 1399, 125, 1, 1, 253, 4863, 19243, 19243, 4863, 253, 1, 1, 509, 16048, 106099, 194846, 106099, 16048, 509, 1, 1, 1021, 51298, 532466, 1622734, 1622734, 532466, 51298]

cp's OEIS Frontend

A157177 A new general triangle sequence based on the Eulerian form in three parts: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)].

Table of values

List of values

cp's OEIS Frontend

A157177 A new general triangle sequence based on the Eulerian form in three parts:m=1; 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

A157177 A new general triangle sequence based on the Eulerian form in three parts: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)].