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A062079 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.

%I A062079 #13 May 13 2022 07:57:33
%S A062079 1,15,693,62985,3151575,706110405,44166438855,30637289555145,
%T A062079 3274769391079725,312250034062131165,593968671422526274875,
%U A062079 5531265959247033940935,95840860214492177176316925
%N A062079 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.
%H A062079 Harry J. Smith, <a href="/A062079/b062079.txt">Table of n, a(n) for n = 1..100</a>
%F A062079 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
%e A062079 a(3) = lcm(7,9,11) = 693.
%t A062079 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 *)
%o A062079 (PARI) a(n) = local(r);r=1;forstep(k=n^2-n+1,n^2+n-1,2,r=lcm(r,k));r \\ _Franklin T. Adams-Watters_, Jul 03 2009
%o A062079 (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
%o A062079 (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
%Y A062079 Cf. A057003, A062032. - _Franklin T. Adams-Watters_, Jul 03 2009
%K A062079 nonn
%O A062079 1,2
%A A062079 _Amarnath Murthy_, Jun 15 2001
%E A062079 Corrected and extended by _Franklin T. Adams-Watters_, Jul 03 2009