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%I #12 Aug 20 2019 03:26:27
%S 0,1,105,5006,360295,39069969,5967561425,1220096908540,
%T 321570878428431,106137499051583495,42873948150095461729,
%U 20803502274492921983130,11938961126118491232766895,7998487694738166709923838621
%N 1-1, 2*3-(2+3), 4*5*6-(4+5+6), 7*8*9*10-(7+8+9+10), ...
%H Harvey P. Dale, <a href="/A075350/b075350.txt">Table of n, a(n) for n = 1..226</a>
%F From _Emeric Deutsch_, Aug 04 2005: (Start)
%F 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].
%F a(n) = [n(n+1)/2]!/[n(n-1)/2]! - n(n^2+1)/2. (End)
%e a(3) = 4*5*6-(4+5+6) = 120-15 = 105.
%p 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
%t Times@@#-Total[#]&/@With[{nn=15},TakeList[Range[(nn(nn+1))/2],Range[ nn]]] (* _Harvey P. Dale_, May 06 2019 *)
%Y Cf. A075351.
%K nonn
%O 1,3
%A _Amarnath Murthy_, Sep 19 2002
%E More terms from _Emeric Deutsch_, Aug 04 2005
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