A156823 - cp's OEIS frontend

A156823 Triangle T(n,k,2) read by rows (generalized q-Stirling numbers of second kind): T(n, k, q_) = (1/(q - 1)^k)Sum[(-1)^(k - j)q*Binomial[k + n, k -j] - Binomial[j + n, j, q - 1], {j, 0, k}], with q=2, where Binomial[,] is the Gaussian q-binomial coefficient as in A022166.

n	a(n)
0	1
1	1
2	1
3	1
4	4
5	13
6	1
7	11
8	90
9	670
10	1
11	26
12	480
13	7870
14	122861
15	1
16	57
17	2247
18	77527
19	2526198
20	80189094
21	1
22	120
23	9807
24	695368
25	46334382
26	2999255160
27	191467330714
28	1
29	247
30	41176
31	5924720
32	798773822
33	104443530554
34	13455795711072
35	1721026866650520
36	1

[1, 1, 1, 1, 4, 13, 1, 11, 90, 670, 1, 26, 480, 7870, 122861, 1, 57, 2247, 77527, 2526198, 80189094, 1, 120, 9807, 695368, 46334382, 2999255160, 191467330714, 1, 247, 41176, 5924720, 798773822, 104443530554, 13455795711072, 1721026866650520, 1]

cp's OEIS Frontend

A156823 Triangle T(n,k,2) read by rows (generalized q-Stirling numbers of second kind): T(n, k, q_) = (1/(q - 1)^k)Sum[(-1)^(k - j)q*Binomial[k + n, k -j] - Binomial[j + n, j, q - 1], {j, 0, k}], with q=2, where Binomial[,] is the Gaussian q-binomial coefficient as in A022166.

Table of values

List of values

cp's OEIS Frontend

A156823 Triangle T(n,k,2) read by rows (generalized q-Stirling numbers of second kind): T(n, k, q_) = (1/(q - 1)^k)*Sum[(-1)^(k - j)*q*Binomial[k + n, k -j] - Binomial[j + n, j, q - 1], {j, 0, k}], with q=2, where Binomial[,] is the Gaussian q-binomial coefficient as in A022166.

Table of values

List of values

A156823 Triangle T(n,k,2) read by rows (generalized q-Stirling numbers of second kind): T(n, k, q_) = (1/(q - 1)^k)Sum[(-1)^(k - j)q*Binomial[k + n, k -j] - Binomial[j + n, j, q - 1], {j, 0, k}], with q=2, where Binomial[,] is the Gaussian q-binomial coefficient as in A022166.