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%I #31 Sep 08 2022 08:45:28
%S 0,-1,-2,-2,8,88,656,4912,40064,362368,3627776,39914752,478997504,
%T 6227012608,87178274816,1307674335232,20922789822464,355687427964928,
%U 6402373705465856,121645100408307712,2432902008175591424,51090942171707342848,1124000727777603485696
%N a(n) = n! - 2^n.
%C Difference between the number of rows in the truth tables for circuit designs involving n variables and the order of S_n (the symmetric group on n symbols).
%D Audu, M. S. and Ibrahim, A. A., (2006) Discrete Mathematics With Applications (in preparation)
%D Ibrahim, A. A., (2006) A stable Variety of Cayley Graphs For Efficient Interconnection Networks (submitted)
%D Ibrahim, A. A. and Audu, M. S., (2005) Some Group theoretic Properties of Certain class of (123) and (132)-avoiding patterns of certain numbers; An enumeration Scheme. African Journal of Natural Sciences, Afri. J. Nat. Sci., 8: 79-84.
%H G. C. Greubel, <a href="/A123642/b123642.txt">Table of n, a(n) for n = 0..445</a>
%F a(n) = A000142(n) - A000079(n). - _Michel Marcus_, Aug 12 2013
%F (-n+3)*a(n) +(n^2-n-4)*a(n-1) -2*(n-1)*(n-2)*a(n-2)=0 for n >= 3. - _R. J. Mathar_, Oct 20 2015; amended by _Georg Fischer_, Mar 13 2020
%F E.g.f.: 1/(1 - x) - exp(2*x). - _G. C. Greubel_, Oct 26 2017
%p f:= gfun:-rectoproc({(-n+3)*a(n) +(n^2-n-4)*a(n-1) -2*(n-1)*(n-2)*a(n-2)=0,
%p a(0)=0, a(1)=-1, a(2)=-2, a(3)=-2}, a(n), remember): map(f, [$0..40]); # _Georg Fischer_, Mar 13 2020
%t Table[n!-2^n,{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, May 19 2011 *)
%o (Sage) [factorial(n)-2^n for n in range(0, 23)] # _Zerinvary Lajos_, Oct 27 2009
%o (PARI) for(n=0,25, print1(n!-2^n, ", ")) \\ _G. C. Greubel_, Oct 17 2017
%o (Magma) [n!-2^n: n in [0..25]]; // _G. C. Greubel_, Oct 17 2017
%K sign,easy
%O 0,3
%A _Aminu Alhaji Ibrahim_, Oct 04 2006
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