%I
%S 1,20,4620,12697776,159845400,941432800,158800433792,1895312483064000,
%T 3438271897004237230080,933561026438040,2562849175892544,
%U 640904462719404383808000,1528364130975,2352733350786,959393282698730880000,6142080926952
%N Let b(0)=0. For n >= 1, b(n) is the least k > b(n1)+1 such that k divides (k1)!/b(n1)!, and a(n) = (b(n)1)!/(b(n1)!*b(n)).
%C Group the natural numbers so that every 2nth group product is divisible by the single number in the next group. (1), (2,3,4,5), (6), (7,8,9,10,11), (12), (13,14,15,16,17,18,19),(20), (21,22,23,24,25,26,27),(28),...Sequence contains the ratio of the product of terms in 2nth group and the (2n+1)th group.
%H Robert Israel, <a href="/A079759/b079759.txt">Table of n, a(n) for n = 1..10001</a> (corrected by Robert Israel, Jan 20 2019)
%e a(1) = 1*2*3*4*5/6 = 20, a(2) = 7*8*9*10*11/12 = 4620, a(3) = 13*14*15*16*17*18*19/20 = 12697776, a(4) = 159845400 = 21*22*...*27/28.
%p t:= 0:
%p for n from 1 to 30 do
%p p:= t+1;
%p for j from t+2 while not (p/j)::integer do p:= p*j od;
%p A[n]:= p/j;
%p t:= j;
%p od:
%p seq(A[i],i=1..30); # _Robert Israel_, Jul 16 2018
%t a[1] = 1; t = 0; nmax = 16; For[n = 1, n <= nmax, n++, p = t+1; For[j = t+2, Not[IntegerQ[p/j]], j++, p = p*j]; a[n+1] = p/j; t = j];
%t Table[a[n], {n, 1, nmax}] (* _JeanFrançois Alcover_, Mar 25 2019, after _Robert Israel_ *)
%Y Cf. A079759, A079760, A109895, A109896, A109897.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Jan 10 2003
%E More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com) and _Sascha Kurz_, Jan 12 2003
%E Edited by _N. J. A. Sloane_, Nov 04 2018 at the suggestion of _Georg Fischer_. This entry now contains the merger of two identical sequences submitted by the same author.
