A083746 a(1) = 1, a(2) = 2; for n>2, a(n) = 3*(n-2)*(n-2)!.

1, 2, 3, 12, 54, 288, 1800, 12960, 105840, 967680, 9797760, 108864000, 1317254400, 17244057600, 242853811200, 3661488230400, 58845346560000, 1004293914624000, 18140058832896000, 345728180109312000, 6933770723303424000

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003

Keywords

• nonn

Comments

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).

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014

Crossrefs

Cf. A001563, A052673, A129379.

Programs

Magma

[n le 2 select n else 3*(n-2)*Factorial(n-2): n in [1..40]]; // G. C. Greubel, Feb 03 2024

Maple

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 Sellers, May 19 2003

Mathematica

Join[{1,2},Table[3n n!,{n,20}]] (* Harvey P. Dale, Feb 27 2012 *)

SageMath

[1,2]+[3*(n-2)*factorial(n-2) for n in range(3, 41)] # G. C. Greubel, Feb 03 2024

Formula

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

E.g.f.: 3*(x-2)*log(1-x) - 5*x + x^2. - Vladeta Jovovic, May 06 2003

From Reinhard Zumkeller, Apr 14 2007: (Start)

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

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

Extensions

Simpler description from Vladeta Jovovic, May 06 2003

More terms from James Sellers, May 19 2003