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a(n) = floor(product_{k=2..n} log(k)).
2

%I #15 Feb 12 2023 06:06:55

%S 0,0,1,1,3,5,12,27,62,149,371,952,2513,6807,18873,53472,154554,455076,

%T 1363287,4150560,12829558,40227005,127843589,411512640,1340747909,

%U 4418886387,14724633149,49582195801,168638834537,579103599979

%N a(n) = floor(product_{k=2..n} log(k)).

%H Vaclav Kotesovec, <a href="/A056690/b056690.txt">Table of n, a(n) for n = 2..1000</a>

%F log(a(n)) ~ n*(log(log(n)) - 1/log(n) - 1/log(n)^2 - 2/log(n)^3 - 6/log(n)^4 - 24/log(n)^5 - ...). - _Vaclav Kotesovec_, Feb 12 2023

%e log(2)*log(3)*log(4)*log(5)= 1.699... So a(5) = 1, since the integer part of 1.699... is 1.

%t Table[Floor[Product[Log[k], {k, 2, n}]], {n, 2, 40}] (* _Vaclav Kotesovec_, Nov 28 2015 *)

%Y Cf. A025201, A046654.

%K easy,nonn

%O 2,5

%A _Leroy Quet_, Aug 10 2000