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a(n) = n(n-1)(n-3)(n-6)...(n-t), where t is the largest triangular number less than n; number of factors in the product is ceiling((sqrt(1+8*n)-1)/2).
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%I #13 Aug 17 2019 08:03:31

%S 1,2,6,12,40,90,168,560,1296,2520,4400,14256,32760,64064,113400,

%T 187200,586432,1321920,2560896,4522000,7484400,11797632,35784320,

%U 78871968,150480000,263120000,433060992,681080400,1033305728,3044304000

%N a(n) = n(n-1)(n-3)(n-6)...(n-t), where t is the largest triangular number less than n; number of factors in the product is ceiling((sqrt(1+8*n)-1)/2).

%e a(8) = 8*(8-1)*(8-3)*(8-6) = 8*7*5*2 = 560.

%p a:=n->product(n-k*(k+1)/2,k=0..ceil((sqrt(1+8*n)-1)/2)-1): seq(a(n),n=1..35); # _Emeric Deutsch_, Feb 03 2006

%Y Cf. A057944, A094262.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Apr 26 2004

%E Corrected and extended by _Emeric Deutsch_, Feb 03 2006