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A139172 a(n) = n!/2 - 1.

%I A139172 #29 Dec 26 2024 02:13:29
%S A139172 0,2,11,59,359,2519,20159,181439,1814399,19958399,239500799,
%T A139172 3113510399,43589145599,653837183999,10461394943999,177843714047999,
%U A139172 3201186852863999,60822550204415999,1216451004088319999,25545471085854719999,562000363888803839999,12926008369442488319999
%N A139172 a(n) = n!/2 - 1.
%C A139172 Natural numbers of the form (n!-m)/m:
%C A139172 for m=1 n!-1 see A033312;
%C A139172 for m=3 (n!-3)/3 see A139173;
%C A139172 for m=4 (n!-4)/4 see A139174;
%C A139172 for m=5 (n!-5)/5 see A139175;
%C A139172 for m=6 (n!-6)/6 see A139176;
%C A139172 for m=7 (n!-7)/7 see A139177;
%C A139172 for m=8 (n!-8)/8 see A139183;
%C A139172 for m=9 (n!-9)/9 see A139184;
%C A139172 for m=10 (n!-10)/10 see A139185.
%C A139172 From _Artur Jasinski_, Oct 14 2008: (Start)
%C A139172 a(n) = Number of numbers removed in first step of Eratosthenes's sieve for n!
%C A139172 a(5)=A145532(1), a(6)=A145533(1), a(7)=A145534(1), a(8)=A145535(1), a(9)=A145536(1), a(10)=A145537(1). (End)
%C A139172 Generally, for n >= m, the formula a(n) = n*(a(n-1) + 1) - 1 applies to all natural numbers of the form (n!-m)/m, m >= 2. - _Bob Selcoe_, Mar 28 2015
%H A139172 Vincenzo Librandi, <a href="/A139172/b139172.txt">Table of n, a(n) for n = 2..300</a>
%F A139172 a(n) = Sum_{k=1..floor(n/2)} s(n,n-2*k), where s(n,k) are Stirling numbers of the first kind, A048994. - _Mircea Merca_, Apr 07 2012
%F A139172 a(n) = n*(a(n-1) + 1) - 1. - _Bob Selcoe_, Mar 28 2015
%t A139172 Table[(n! - 2)/2, {n, 2, 20}]
%o A139172 (Magma) [(Factorial(n)-2)/2: n in [2..25]]; // _Vincenzo Librandi_, Jul 20 2011
%o A139172 (PARI) a(n)=n!/2-1 \\ _Charles R Greathouse IV_, Apr 07 2012
%Y A139172 Cf. A033312, A139173, A139174, A139175, A139176, A139177, A139183, A139184.
%K A139172 nonn,easy
%O A139172 2,2
%A A139172 _Artur Jasinski_, Apr 11 2008