A075350 1-1, 2*3-(2+3), 4*5*6-(4+5+6), 7*8*9*10-(7+8+9+10), ...

0, 1, 105, 5006, 360295, 39069969, 5967561425, 1220096908540, 321570878428431, 106137499051583495, 42873948150095461729, 20803502274492921983130, 11938961126118491232766895, 7998487694738166709923838621

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..226

Formula

From Emeric Deutsch, Aug 04 2005: (Start)

a(n) = product[j, j=n(n-1)/2+1..n(n+1)/2] - sum[j, j=n(n-1)/2+1..n(n+1)/2].

a(n) = [n(n+1)/2]!/[n(n-1)/2]! - n(n^2+1)/2. (End)

Example

a(3) = 4*5*6-(4+5+6) = 120-15 = 105.

Maple

a:=n->(n*(n+1)/2)!/(n*(n-1)/2)!-n*(n^2+1)/2: seq(a(n), n=1..16); # Emeric Deutsch, Aug 04 2005

Mathematica

Times@@#-Total[#]&/@With[{nn=15}, TakeList[Range[(nn(nn+1))/2], Range[ nn]]] (* Harvey P. Dale, May 06 2019 *)

Crossrefs

Cf. A075351.

Sequence in context: A360275 A221791 A210138 * A165055 A168306 A075914

Adjacent sequences: A075347 A075348 A075349 * A075351 A075352 A075353

Keyword

nonn

Author

Amarnath Murthy, Sep 19 2002

Extensions

More terms from Emeric Deutsch, Aug 04 2005

Status

approved