The On-Line Encyclopedia of Integer Sequences (OEIS)

A345466 revision #14

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

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OFFSET

0,3

LINKS

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

FORMULA

Conjecture: 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 *)

CROSSREFS