A308820 a(n) = Product_{k=1..n} ceiling(n/k)!.

1, 2, 12, 96, 2880, 34560, 5806080, 92897280, 25082265600, 2006581248000, 794606174208000, 19070548180992000, 208250386136432640000, 5831010811820113920000, 4198327784510482022400000, 3224315738504050193203200000, 14799609239733590386802688000000

Offset: 1

Author

Ilya Gutkovskiy, Jun 26 2019

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..178

Crossrefs

Cf. A010786, A020696, A092143, A131385.

Programs

Magma

[(&*[Factorial(Ceiling(n/(n-j+1))): j in [1..n]]): n in [1..20]]; // G. C. Greubel, Mar 08 2023

Maple

seq(mul(ceil(n/k)!, k=1..n), n=1..30); # Ridouane Oudra, Apr 10 2023

Mathematica

a[n_] := Product[Ceiling[n/k]!, {k, 1, n}]; Table[a[n], {n, 1, 17}]

PARI

a(n) = prod(k=1, n, ceil(n/k)!); \\ Michel Marcus, Jun 27 2019

SageMath

def A308820(n): return product( factorial(ceil(n/(n-k+1))) for k in range(1,n+1))
[A308820(n) for n in range(1,21)] # G. C. Greubel, Mar 08 2023

Formula

a(n) = Product_{k=1..n-1} Product_{d|k} (d + 1).

a(n) = Product_{k=1..n-1} (k + 1)^floor((n-1)/k). - Ridouane Oudra, Apr 10 2023

a(n) = A131385(n)*A092143(n-1). - Ridouane Oudra, Sep 20 2024