A156586 - cp's OEIS frontend

A156586 A new q-combination type general triangle sequence based on Stirling first polynomials: here q=4: m=3: 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	4
5	1
6	1
7	20
8	20
9	1
10	1
11	120
12	600
13	120
14	1
15	1
16	840
17	25200
18	25200
19	840
20	1
21	1
22	6720
23	1411200
24	8467200
25	1411200
26	6720
27	1
28	1
29	60480
30	101606400
31	4267468800
32	4267468800
33	101606400
34	60480
35	1
36	1
37	604800
38	9144576000
39	3072577536000
40	21508042752000

[1, 1, 1, 1, 4, 1, 1, 20, 20, 1, 1, 120, 600, 120, 1, 1, 840, 25200, 25200, 840, 1, 1, 6720, 1411200, 8467200, 1411200, 6720, 1, 1, 60480, 101606400, 4267468800, 4267468800, 101606400, 60480, 1, 1, 604800, 9144576000, 3072577536000, 21508042752000]

cp's OEIS Frontend

A156586 A new q-combination type general triangle sequence based on Stirling first polynomials: here q=4: m=3: 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

A156586 A new q-combination type general triangle sequence based on Stirling first polynomials: here q=4: m=3: 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

A156586 A new q-combination type general triangle sequence based on Stirling first polynomials: here q=4: m=3: 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])].