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%I #12 Oct 22 2014 16:25:14
%S 1,2,6,3,7,42,1512,2000376,3556892570112,11386336279786153952123289,
%T 117862412614885811248635740101130996768076206774085
%N a(n) = n! for n < 4; else a(n) = floor(P(n-1)/n) where P(n) = a(1) * a(2) * ... * a(n).
%C Original definition: a(1)=1, a(n)=n*P(n-1) if P(n-1) < n, a(n) = floor(P(n-1)/n) if n <= P(n-1), where P(n-1) = a(1) * a(2) * ... * a(n-1).
%C Next term a(12) = 1273391928...9197035520 ~ 1.27*10^100 has 101 digits. - _M. F. Hasler_, Oct 21 2014
%e a(4) = floor(1*2*6/4) = 3.
%e a(5) = floor(1*2*6*3/5) = floor(36/5) = 7.
%t a[1] = 1; p[n_] := Product[a[k], {k, 1, n}]; a[n_ /; p[n-1] < n] := a[n] = n*p[n-1]; a[n_ /; n < p[n-1]] := a[n] = Floor[p[n-1]/n]; Table[a[n], {n, 1, 12}] (* _Jean-François Alcover_, Jul 22 2013 *)
%o (PARI) a(n)=if(n<4,n!,P=3!;for(i=3,n-1,P*=P\i);P\n) \\ _M. F. Hasler_, Oct 21 2014
%Y Cf. A076039, A003462, A076042, A046901.
%K nice,nonn,easy
%O 1,2
%A _Amarnath Murthy_, Oct 29 2002
%E Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003
%E Edited by _M. F. Hasler_, Oct 21 2014
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