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A161887 A product of quotients of factorials. 1

%I

%S 1,2,6,12,60,120,840,7560,15120,110880,166320,1441440,2882880,

%T 10810800,43243200,183783600,367567200,2793510720,6983776800,

%U 58663725120,117327450240,299836817280,2698531355520,7495920432000

%N A product of quotients of factorials.

%C Definition: Let b(n,k) = floor(n/2^k)! and m = log[2](n) then c(n) = product_{k=1..m} b(n,k) / b(n,k+1)^2.

%C a(n) is the sequence derived from c(n) by eliminating duplicates and sorting the values.

%C a(1) through a(19) are highly composite numbers (A002182).

%C The number of divisors of a(1) through a(28) are number of divisors of highly composite numbers (A002183).

%C A055773(floor(n/2)) is a divisor of a(n), a(n)/A055773(floor(n/2)) after eliminating duplicates and sorting starts 1,4,24,216,1440,2160,..

%H Amiram Eldar, <a href="/A161887/b161887.txt">Table of n, a(n) for n = 1..1669</a>

%p a := proc(n) local m,k; m := nops(convert(n,base,2));

%p mul(iquo(n,2^k)!/iquo(n,2^(k+1))!^2,k=1..m-1) end:

%p seq(a(i),i=1..50): A:=sort(convert({%},list));

%t b[n_, k_] := Floor[n/2^k]!; c[n_] := Product[b[n, k]/b[n, k+1]^2, {k, 1, Log[2, n]}]; A = Array[c, 50] // DeleteDuplicates // Sort (* _Jean-Fran├žois Alcover_, Jun 17 2019 *)

%Y Cf. A002182, A002183.

%K easy,nonn

%O 1,2

%A _Peter Luschny_, Jun 21 2009

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Last modified July 23 19:17 EDT 2021. Contains 346259 sequences. (Running on oeis4.)