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A359365
a(n) = lcm([ n!*binomial(n-1, m-1) / m! for m = 1..n ]) with a(0) = 1.
1
1, 1, 2, 6, 72, 240, 3600, 75600, 1411200, 10160640, 457228800, 4191264000, 184415616000, 2054916864000, 12466495641600, 1308982042368000, 314155690168320000, 14241724620963840000, 2178983867007467520000, 37260624125827694592000, 337119932567012474880000
OFFSET
0,3
COMMENTS
The lcm of the rows of the unsigned Lah triangle (for k >= 1).
LINKS
MAPLE
# Maple has the convention integer lcm() = 1, which covers the case n = 0.
a := n -> ilcm(seq(n!*binomial(n-1, m-1) / m!, m = 1..n)):
seq(a(n), n = 0..20);
MATHEMATICA
{1}~Join~Table[LCM @@ Array[n!*Binomial[n - 1, # - 1]/#! &, n], {n, 20}] (* Michael De Vlieger, Dec 30 2022 *)
PROG
(Python)
from functools import cache
from sympy import lcm
def A359365 (n: int) -> int:
@cache
def l(n: int) -> list[int]:
if n == 0: return [1]
row: list[int] = l(n - 1) + [1]
row[0] = 0
for k in range(n - 1, 0, -1):
row[k] = row[k] * (n + k - 1) + row[k - 1]
return row
return lcm(l(n)[1:])
print([A359365(n) for n in range(21)])
(PARI) a(n) = lcm(vector(n, m, n!*binomial(n-1, m-1) / m!)); \\ Michel Marcus, Dec 30 2022
CROSSREFS
Cf. A271703 (unsigned Lah numbers), A103505 (gcd counterpart).
Sequence in context: A239543 A180982 A195690 * A329965 A171582 A152885
KEYWORD
nonn
AUTHOR
Peter Luschny, Dec 30 2022
STATUS
approved