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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
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
Sequence in context: A290149 A187083 A114184 * A265869 A274083 A079183
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Apr 22 2004
EXTENSIONS
More terms from Vladeta Jovovic, May 27 2004
STATUS
approved

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