A350268
a(n) = Sum_{k=0..n} (n - k)! * (n - 1)^k. Row sums of A350269.
Original entry on oeis.org
1, 1, 4, 22, 168, 1720, 22670, 368784, 7134148, 159416704, 4027395330, 113235212800, 3501763366904, 118024658758656, 4303855119215782, 168777440194263040, 7081468496171815500, 316501174908316647424, 15010862087643791689322, 752916261526858377363456
Offset: 0
-
a[1] = 1; a[n_] := Sum[(n - k)! * (n - 1)^k, {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Dec 25 2021 *)
-
a(n) = sum(k=0, n, (n-k)!*(n-1)^k); \\ Michel Marcus, Dec 25 2021
A350297
Triangle read by rows: T(n,k) = n!*(n-1)^k/k!.
Original entry on oeis.org
1, 1, 0, 2, 2, 1, 6, 12, 12, 8, 24, 72, 108, 108, 81, 120, 480, 960, 1280, 1280, 1024, 720, 3600, 9000, 15000, 18750, 18750, 15625, 5040, 30240, 90720, 181440, 272160, 326592, 326592, 279936, 40320, 282240, 987840, 2304960, 4033680, 5647152, 6588344, 6588344, 5764801
Offset: 0
Triangle T(n,k) begins:
-----------------------------------------------------------------
n\k 0 1 2 3 4 5 6 7
-----------------------------------------------------------------
0 | 1,
1 | 1, 0,
2 | 2, 2, 1,
3 | 6, 12, 12, 8,
4 | 24, 72, 108, 108, 81,
5 | 120, 480, 960, 1280, 1280, 1024,
6 | 720, 3600, 9000, 15000, 18750, 18750, 15625,
7 | 5040, 30240, 90720, 181440, 272160, 326592, 326592, 279936.
...
-
T := (n, k) -> (n!/k!)*(n - 1)^k:
seq(seq(T(n, k), k = 0..n), n = 0..8); # Peter Luschny, Dec 24 2021
-
T[1, 0] := 1; T[n_, k_] := n!*(n - 1)^k/k!; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, Dec 24 2021 *)
Showing 1-2 of 2 results.
Comments