The On-Line Encyclopedia of Integer Sequences (OEIS)

A345466 revision #21

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

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

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

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 *)

PROG

(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

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

CROSSREFS

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

Sequence in context: A106343 A086992 A354316 * A115965 A001142 A111847

Adjacent sequences: A345463 A345464 A345465 * A345467 A345468 A345469

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jun 20 2021

STATUS

approved