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a(1) = 1; a(n) = n!*(3/2) for n>=2.
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%I #34 Apr 15 2024 13:12:33

%S 1,3,9,36,180,1080,7560,60480,544320,5443200,59875200,718502400,

%T 9340531200,130767436800,1961511552000,31384184832000,533531142144000,

%U 9603560558592000,182467650613248000,3649353012264960000,76636413257564160000,1686001091666411520000,38778025108327464960000

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

%C 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

%C 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 +, -, *, /.

%H Reinhard Zumkeller, <a href="/A070960/b070960.txt">Table of n, a(n) for n = 1..400</a>

%H Jun Yan, <a href="https://arxiv.org/abs/2404.07958">Results on pattern avoidance in parking functions</a>, arXiv:2404.07958 [math.CO], 2024. See p. 4.

%H <a href="/index/Fo#4x4">Index entries for similar sequences</a>.

%F E.g.f.: x*(2+x)/(1-x)/2. - _Vladeta Jovovic_, Dec 15 2002

%F a(n) = A245334(n,n-2), n > 1. - _Reinhard Zumkeller_, Aug 31 2014

%F From _Amiram Eldar_, Jan 15 2023: (Start)

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

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

%F a(n) = A000142(n) + A001710(n) for n>=2. - _Alois P. Heinz_, Feb 20 2024

%e 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.

%t 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 *)

%t Join[{1},(3*Range[2,20]!)/2] (* _Harvey P. Dale_, Jun 15 2022 *)

%o (Haskell)

%o a070960 n = if n == 1 then 1 else 3 * a000142 n `div` 2

%o a070960_list = map (flip div 2) fs where fs = 3 : zipWith (*) [2..] fs

%o -- _Reinhard Zumkeller_, Aug 31 2014

%o (PARI) a(n) = if (n==1, 1, n!*3/2); \\ _Michel Marcus_, Dec 03 2022

%Y Cf. A000142, A001710, A060315.

%Y Cf. A245334.

%K easy,nonn

%O 1,2

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

%E Edited by _N. J. A. Sloane_, Jul 22 2009