cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A161887 A product of quotients of factorials.

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%I A161887 #9 Aug 20 2019 09:23:47
%S A161887 1,2,6,12,60,120,840,7560,15120,110880,166320,1441440,2882880,
%T A161887 10810800,43243200,183783600,367567200,2793510720,6983776800,
%U A161887 58663725120,117327450240,299836817280,2698531355520,7495920432000
%N A161887 A product of quotients of factorials.
%C A161887 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 A161887 a(n) is the sequence derived from c(n) by eliminating duplicates and sorting the values.
%C A161887 a(1) through a(19) are highly composite numbers (A002182).
%C A161887 The number of divisors of a(1) through a(28) are number of divisors of highly composite numbers (A002183).
%C A161887 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 A161887 Amiram Eldar, <a href="/A161887/b161887.txt">Table of n, a(n) for n = 1..1669</a>
%p A161887 a := proc(n) local m,k; m := nops(convert(n,base,2));
%p A161887 mul(iquo(n,2^k)!/iquo(n,2^(k+1))!^2,k=1..m-1) end:
%p A161887 seq(a(i),i=1..50): A:=sort(convert({%},list));
%t A161887 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-François Alcover_, Jun 17 2019 *)
%Y A161887 Cf. A002182, A002183.
%K A161887 easy,nonn
%O A161887 1,2
%A A161887 _Peter Luschny_, Jun 21 2009