A360283 a(n) = lcm({n! * binomial(n, k) for k = 0..n}).

1, 1, 4, 18, 288, 1200, 43200, 529200, 11289600, 91445760, 9144576000, 92207808000, 13277924352000, 160283515392000, 2094371267788800, 58904191906560000, 15079473128079360000, 242109318556385280000, 78443419212268830720000, 1415903716781452394496000

Offset: 0

Author

Peter Luschny, Feb 14 2023

Keywords

• nonn

Crossrefs

Cf. A002397, A003418 (LCM), A005722, A021012, A196347.

Programs

Maple

a := n -> ilcm(seq(n!*binomial(n, k), k=0..n)):
seq(a(n), n = 0..19);

Python

from math import factorial, lcm
def A360283(n): return factorial(n)*lcm(*(i for i in range(1,n+2)))//(n+1) # Chai Wah Wu, Feb 15 2023

Formula

a(n) = n! * lcm({k for k = 1..n+1}) / (n+1) = n! * LCM(n + 1) / (n + 1).

a(n) / a(n-1) = n^2 if and only if n + 1 is prime, for n >= 1.