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A062079
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Group the odd numbers as (1), (3,5), (7,9,11), (13,15,17,19), (21,23,25,27,29), ... then a(n) = LCM of the n-th group.
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1
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1, 15, 693, 62985, 3151575, 706110405, 44166438855, 30637289555145, 3274769391079725, 312250034062131165, 593968671422526274875, 5531265959247033940935, 95840860214492177176316925
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = lcm(Gamma(2*binomial(n+1, 2) + 1)*Gamma(binomial(n, 2) + 1)/(2^n*Gamma(binomial(n+1, 2) + 1)*Gamma(2*binomial(n, 2) + 1))). - G. C. Greubel, May 13 2022
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EXAMPLE
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a(3) = lcm(7,9,11) = 693.
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MATHEMATICA
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Table[LCM[Gamma[2*Binomial[n+1, 2] + 1]*Gamma[Binomial[n, 2] + 1]/(2^n*Gamma[Binomial[n+1, 2] + 1]*Gamma[2*Binomial[n, 2] + 1])], {n, 20}] (* G. C. Greubel, May 13 2022 *)
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PROG
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(PARI) { for (n=1, 100, a=b=n^2 - n + 1; for (k=1, n - 1, a=lcm(a, b + 2*k)); write("b062079.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 31 2009
(SageMath) [lcm(gamma(2*binomial(n+1, 2) + 1)*gamma(binomial(n, 2) + 1)/(2^n*gamma(binomial(n+1, 2) + 1)*gamma(2*binomial(n, 2) + 1))) for n in (1..20)] # G. C. Greubel, May 13 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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