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.

1, 15, 693, 62985, 3151575, 706110405, 44166438855, 30637289555145, 3274769391079725, 312250034062131165, 593968671422526274875, 5531265959247033940935, 95840860214492177176316925

Offset: 1

Author

Amarnath Murthy, Jun 15 2001

Keywords

• nonn

Examples

			a(3) = lcm(7,9,11) = 693.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A057003, A062032. - Franklin T. Adams-Watters, Jul 03 2009

Programs

Mathematica

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 *)

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

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

Formula

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

Extensions

Corrected and extended by Franklin T. Adams-Watters, Jul 03 2009