A354042 - cp's OEIS frontend

A354042 Triangle read by rows. The Faulhaber numbers. F(0, k) = 1 and otherwise F(n, k) = (n + 1)!(-1)^(k+1)Sum_{j=0..floor((k-1)/2)} C(2k-2j, k+1)C(2n+1, 2j+1) Bernoulli(2n-2j) / (k - j).

n	a(n)
0	1
1	0
2	1
3	0
4	-1
5	2
6	0
7	4
8	-8
9	6
10	0
11	-36
12	72
13	-60
14	24
15	0
16	600
17	-1200
18	1020
19	-480
20	120
21	0
22	-16584
23	33168
24	-28320
25	13776
26	-4200
27	720
28	0
29	705600
30	-1411200
31	1206240
32	-591360
33	188160
34	-40320
35	5040
36	0
37	-43751232
38	87502464
39	-74813760
40	36747648
41	-11813760
42	2661120
43	-423360
44	40320

[1, 0, 1, 0, -1, 2, 0, 4, -8, 6, 0, -36, 72, -60, 24, 0, 600, -1200, 1020, -480, 120, 0, -16584, 33168, -28320, 13776, -4200, 720, 0, 705600, -1411200, 1206240, -591360, 188160, -40320, 5040, 0, -43751232, 87502464, -74813760, 36747648, -11813760, 2661120, -423360, 40320]

cp's OEIS Frontend

A354042 Triangle read by rows. The Faulhaber numbers. F(0, k) = 1 and otherwise F(n, k) = (n + 1)!(-1)^(k+1)Sum_{j=0..floor((k-1)/2)} C(2k-2j, k+1)C(2n+1, 2j+1) Bernoulli(2n-2j) / (k - j).

Table of values

List of values

cp's OEIS Frontend

A354042 Triangle read by rows. The Faulhaber numbers. F(0, k) = 1 and otherwise F(n, k) = (n + 1)!*(-1)^(k+1)*Sum_{j=0..floor((k-1)/2)} C(2*k-2*j, k+1)*C(2*n+1, 2*j+1) * Bernoulli(2*n-2*j) / (k - j).

Table of values

List of values

A354042 Triangle read by rows. The Faulhaber numbers. F(0, k) = 1 and otherwise F(n, k) = (n + 1)!(-1)^(k+1)Sum_{j=0..floor((k-1)/2)} C(2k-2j, k+1)C(2n+1, 2j+1) Bernoulli(2n-2j) / (k - j).