A156587 - cp's OEIS frontend

A156587 A new q-combination type general triangle sequence based on Stirling first polynomials: here q=5: m=4: t(n,k)=If[m == 0, n!, Product[Sum[(-1)^(i + k)StirlingS1[k - 1, i](m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].

n	a(n)
0	1
1	1
2	1
3	1
4	5
5	1
6	1
7	30
8	30
9	1
10	1
11	210
12	1260
13	210
14	1
15	1
16	1680
17	70560
18	70560
19	1680
20	1
21	1
22	15120
23	5080320
24	35562240
25	5080320
26	15120
27	1
28	1
29	151200
30	457228800
31	25604812800
32	25604812800
33	457228800
34	151200
35	1
36	1
37	1663200
38	50295168000
39	25348764672000

[1, 1, 1, 1, 5, 1, 1, 30, 30, 1, 1, 210, 1260, 210, 1, 1, 1680, 70560, 70560, 1680, 1, 1, 15120, 5080320, 35562240, 5080320, 15120, 1, 1, 151200, 457228800, 25604812800, 25604812800, 457228800, 151200, 1, 1, 1663200, 50295168000, 25348764672000]

cp's OEIS Frontend

A156587 A new q-combination type general triangle sequence based on Stirling first polynomials: here q=5: m=4: t(n,k)=If[m == 0, n!, Product[Sum[(-1)^(i + k)StirlingS1[k - 1, i](m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].

Table of values

List of values

cp's OEIS Frontend

A156587 A new q-combination type general triangle sequence based on Stirling first polynomials: here q=5: m=4: t(n,k)=If[m == 0, n!, Product[Sum[(-1)^(i + k)*StirlingS1[k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].

Table of values

List of values

A156587 A new q-combination type general triangle sequence based on Stirling first polynomials: here q=5: m=4: t(n,k)=If[m == 0, n!, Product[Sum[(-1)^(i + k)StirlingS1[k - 1, i](m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].