A345466 a(n) = Product_{k=1..n} binomial(n, floor(n/k)).

1, 1, 2, 9, 96, 1250, 64800, 1764735, 224788480, 22499086176, 6123600000000, 408514437465750, 1308805762115174400, 133962125607455951520, 99335199198879310098432, 113040832521732593994140625, 425230288403106927476736000000, 72623663171934137824096600064000

Offset: 0

Author

Vaclav Kotesovec, Jun 20 2021

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..160

Crossrefs

Cf. A010786, A034841, A051054, A092143, A272093.

Programs

Magma

[n eq 0 select 1 else (&*[Binomial(n,Floor(n/j)): j in [1..n]]): n in [0..30]]; // G. C. Greubel, Feb 05 2024

Mathematica

Table[Product[Binomial[n, Floor[n/k]], {k, 1, n}], {n, 0, 20}]
Table[Product[((n + 1)/k - 1)^Floor[n/k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 24 2021 *)

SageMath

[product(binomial(n,(n//j)) for j in range(1,n+1)) for n in range(31)] # G. C. Greubel, Feb 05 2024

Formula

log(a(n)) ~ n * log(n)^2 / 2. - Vaclav Kotesovec, Jun 21 2021

a(n) = Product_{k=1..n} ((n+1)/k - 1)^floor(n/k). - Vaclav Kotesovec, Jun 24 2021