A070960 a(1) = 1; a(n) = n!*(3/2) for n>=2.

1, 3, 9, 36, 180, 1080, 7560, 60480, 544320, 5443200, 59875200, 718502400, 9340531200, 130767436800, 1961511552000, 31384184832000, 533531142144000, 9603560558592000, 182467650613248000, 3649353012264960000, 76636413257564160000, 1686001091666411520000, 38778025108327464960000

Offset: 1

Author

Koksal Karakus (karakusk(AT)hotmail.com), May 24 2002

Keywords

• easy
• nonn

Comments

Let g be a permutation of [1..n] having, say, j_i cycles of length i, with Sum_i i*j_i = n; sequence gives Sum_{g} Sum_{i} (j_1 + j_2). - N. J. A. Sloane, Jul 22 2009

a(n) is the greatest integer that can be obtained from the integers {1, 2, 3, ..., n} using each number at most once and the operators +, -, *, /.

Examples

			a(5) = 180 because the greatest number we can obtain using 1, 2, 3, 4, 5 is 180 which is (1+2)*3*4*5.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..400
• Jun Yan, Results on pattern avoidance in parking functions, arXiv:2404.07958 [math.CO], 2024. See p. 4.
• Index entries for similar sequences.

Crossrefs

Cf. A000142, A001710, A060315.

Cf. A245334.

Programs

Haskell

a070960 n = if n == 1 then 1 else 3 * a000142 n `div` 2
a070960_list = map (flip div 2) fs where fs = 3 : zipWith (*) [2..] fs
-- Reinhard Zumkeller, Aug 31 2014

Mathematica

s=3;lst={1, s};Do[s+=n*s+s;AppendTo[lst, s], {n, 1, 5!, 1}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
Join[{1},(3*Range[2,20]!)/2] (* Harvey P. Dale, Jun 15 2022 *)

PARI

a(n) = if (n==1, 1, n!*3/2); \\ Michel Marcus, Dec 03 2022

Formula

E.g.f.: x*(2+x)/(1-x)/2. - Vladeta Jovovic, Dec 15 2002

a(n) = A245334(n,n-2), n > 1. - Reinhard Zumkeller, Aug 31 2014

From Amiram Eldar, Jan 15 2023: (Start)

Sum_{n>=1} 1/a(n) = (2*e-1)/3.

Sum_{n>=1} (-1)^(n+1)/a(n) = 1 - 2/(3*e). (End)

a(n) = A000142(n) + A001710(n) for n>=2. - Alois P. Heinz, Feb 20 2024

Extensions

Edited by N. J. A. Sloane, Jul 22 2009