%I #29 Feb 03 2024 11:01:06

%S 1,2,3,12,54,288,1800,12960,105840,967680,9797760,108864000,

%T 1317254400,17244057600,242853811200,3661488230400,58845346560000,

%U 1004293914624000,18140058832896000,345728180109312000,6933770723303424000

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

%C a(1) = 1, a(2) = 2, define S(k) = sum of all the terms other than a(k) k < n. a(n) = Sum_{k=1..n-1} S(k).

%H Vincenzo Librandi, <a href="/A083746/b083746.txt">Table of n, a(n) for n = 1..200</a>

%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081, 2014

%F a(n) = (n-2)*Sum_{j=1..n-1} a(j).

%F E.g.f.: 3*(x-2)*log(1-x) - 5*x + x^2. - _Vladeta Jovovic_, May 06 2003

%F From _Reinhard Zumkeller_, Apr 14 2007: (Start)

%F Sum_{k=1..n} a(k) = A052560(n-1) for n > 1.

%F a(n) = A052673(n-2) for n > 2. (End)

%e a(4) = {a(1) + a(2)} + {a(1) +a(3)} + {a(2) + a(3)} = 12.

%p a := proc(n) option remember: if n=1 then RETURN(1) fi: if n=2 then RETURN(2) fi: 3*(n-2)*(n-2)! end: for n from 1 to 40 do printf(`%d,`,a(n)) od: # _James A. Sellers_, May 19 2003

%t Join[{1,2},Table[3n n!,{n,20}]] (* _Harvey P. Dale_, Feb 27 2012 *)

%o (Magma) [n le 2 select n else 3*(n-2)*Factorial(n-2): n in [1..40]]; // _G. C. Greubel_, Feb 03 2024

%o (SageMath) [1,2]+[3*(n-2)*factorial(n-2) for n in range(3, 41)] // _G. C. Greubel_, Feb 03 2024

%Y Cf. A001563, A052673, A129379.

%K nonn

%O 1,2

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003

%E Simpler description from _Vladeta Jovovic_, May 06 2003

%E More terms from _James A. Sellers_, May 19 2003