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A263673
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a(n) = lcm{1,2,...,n} / binomial(n,floor(n/2)).
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3
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1, 1, 1, 2, 2, 6, 3, 12, 12, 20, 10, 60, 30, 210, 105, 56, 56, 504, 252, 2520, 1260, 660, 330, 3960, 1980, 5148, 2574, 4004, 2002, 30030, 15015, 240240, 240240, 123760, 61880, 31824, 15912, 302328, 151164, 77520, 38760, 813960, 406980, 8953560, 4476780, 2288132, 1144066, 27457584, 13728792, 49031400
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OFFSET
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0,4
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COMMENTS
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If n = 2^k, a(n) = a(n-1).
If n = p^k where p is an odd prime and k >= 1, 2*n*a(n) = p*(n+1)*a(n-1).
If n is even and not a prime power, 2*a(n) = a(n-1).
If n is odd and not a prime power, 2*n*a(n) = (n+1)*a(n-1). (End)
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LINKS
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FORMULA
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MAPLE
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a := n -> lcm(seq(k, k=1..n))/binomial(n, iquo(n, 2)):
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MATHEMATICA
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Join[{1}, Table[LCM @@ Range[n]/Binomial[n, Floor[n/2]], {n, 1, 50}]] (* or *) Table[Product[Cyclotomic[k, 1], {k, 2, n}]/Binomial[n, Floor[n/2]], {n, 0, 50}] (* G. C. Greubel, Apr 17 2017 *)
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PROG
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(PARI) A263673(n) = lcm(vector(n, i, i)) / binomial(n, n\2);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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