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Search: id:A161887
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| A161887 |
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A product of quotients of factorials. |
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+0
1
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| 1, 2, 6, 12, 60, 120, 840, 7560, 15120, 110880, 166320, 1441440, 2882880, 10810800, 43243200, 183783600, 367567200, 2793510720, 6983776800, 58663725120, 117327450240, 299836817280, 2698531355520, 7495920432000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
a(n) is the sequence derived from c(n) by eliminating duplicates and sorting the values.
a(1) through a(19) are highly composite numbers (A002182).
The number of divisors of a(1) through a(28) are number of divisors of highly composite numbers (A002183).
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,..
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MAPLE
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a := proc(n) local m, k; m := nops(convert(n, base, 2));
mul(iquo(n, 2^k)!/iquo(n, 2^(k+1))!^2, k=1..m-1) end:
seq(a(i), i=1..50): A:=sort(convert({%}, list));
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CROSSREFS
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Cf. A002182, A002183.
Sequence in context: A096123 A081125 A138570 this_sequence A139315 A014767 A002319
Adjacent sequences: A161884 A161885 A161886 this_sequence A161888 A161889 A161890
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KEYWORD
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easy,nonn
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AUTHOR
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Peter Luschny (peter(AT)luschny.de), Jun 21 2009
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