A123642 a(n) = n! - 2^n.

0, -1, -2, -2, 8, 88, 656, 4912, 40064, 362368, 3627776, 39914752, 478997504, 6227012608, 87178274816, 1307674335232, 20922789822464, 355687427964928, 6402373705465856, 121645100408307712, 2432902008175591424, 51090942171707342848, 1124000727777603485696

Offset: 0

Author

Aminu Alhaji Ibrahim, Oct 04 2006

Keywords

• sign
• easy

Comments

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).

References

• Audu, M. S. and Ibrahim, A. A., (2006) Discrete Mathematics With Applications (in preparation)
• Ibrahim, A. A., (2006) A stable Variety of Cayley Graphs For Efficient Interconnection Networks (submitted)
• 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.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..445

Programs

Magma

[Factorial(n)-2^n: n in [0..25]]; // G. C. Greubel, Oct 17 2017

Maple

f:= gfun:-rectoproc({(-n+3)*a(n) +(n^2-n-4)*a(n-1) -2*(n-1)*(n-2)*a(n-2)=0,
a(0)=0, a(1)=-1, a(2)=-2, a(3)=-2}, a(n), remember): map(f, [$0..40]); # Georg Fischer, Mar 13 2020

Mathematica

Table[n!-2^n,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)

PARI

for(n=0,25, print1(n!-2^n, ", ")) \\ G. C. Greubel, Oct 17 2017

Sage

[factorial(n)-2^n for n in range(0, 23)] # Zerinvary Lajos, Oct 27 2009

Formula

a(n) = A000142(n) - A000079(n). - Michel Marcus, Aug 12 2013

(-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

E.g.f.: 1/(1 - x) - exp(2*x). - G. C. Greubel, Oct 26 2017