The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A093884 Product of all possible sums of three numbers taken from among first n natural numbers. 4
 6, 3024, 2874009600, 159950125679984640000, 20708778572935434707683938140160000000, 302101709923756073800654275737927385319576932502732800000000000 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 21 21:50 EDT 2024. Contains 373559 sequences. (Running on oeis4.)