A093884 Product of all possible sums of three numbers taken from among first n natural numbers.

6, 3024, 2874009600, 159950125679984640000, 20708778572935434707683938140160000000, 302101709923756073800654275737927385319576932502732800000000000

Offset

3,1

References

Amarnath Murthy, Another combinatorial approach towards generalizing the AM GM inequality, Octogon Mathematical Magazine Vol. 8, No. 2, October 2000.

Amarnath Murthy, Smarandache Dual Symmetric Functions And Corresponding Numbers Of The Type Of Stirling Numbers Of The First Kind. Smarandache Notions Journal Vol. 11, No. 1-2-3 Spring 2000.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 3..17

Formula

a(n) ~ sqrt(Pi/A) * 2^(5/12 - n/4 - n^2 - 2*n^3/3) * 3^(-1/6 - 7*n/24 + 3*n^3/4) * exp(1/24 - n/3 + 3*n^2/4 - 11*n^3/36 + zeta(3)/(48*Pi^2)) * n^(11/24 + n/3 - n^2/2 + n^3/6), where A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Aug 31 2023

Example

a(4) = (1+2+3)*(1+2+4)*(1+3+4)*(2+3+4) = 3024.

Mathematica

Table[Product[(j + k + m), {k, 2, n}, {j, 1, k - 1}, {m, 1, j - 1}], {n, 3, 10}] (* Vaclav Kotesovec, Aug 31 2023 *)
Table[Product[Sqrt[BarnesG[3*k] * BarnesG[k+2] * Gamma[k/2 + 1] / Gamma[3*k/2]] / (BarnesG[2*k + 1] * 2^((k-1)/2)), {k, 1, n}], {n, 3, 10}] (* Vaclav Kotesovec, Aug 31 2023 *)

Crossrefs

Cf. A093883, A306594.

Sequence in context: A290149 A187083 A114184 * A265869 A274083 A079183

Adjacent sequences: A093881 A093882 A093883 * A093885 A093886 A093887

Keyword

nonn

Author

Amarnath Murthy, Apr 22 2004

Extensions

More terms from Vladeta Jovovic, May 27 2004

Status

approved