OFFSET
0,5
COMMENTS
a(n) is the number of ways that n people can form two distinct committees and then choose a president and vice president for each committee.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 753.
FORMULA
E.g.f.: x^4*exp(x)^2.
a(n) = A090802(n, 4).
Recurrence: {a(1)=0, a(2)=0, a(3)=0, a(4)=24, (-2*n-2)*a(n)+(n-3)*a(n+1)}.
O.g.f.: -24*x^4/(2*x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009
a(n) = (n-3)*(n-2)*(n-1)*n * 2^(n-4). - Vaclav Kotesovec, Nov 27 2012
From Amiram Eldar, Jan 09 2022: (Start)
Sum_{n>=4} 1/a(n) = 5/18 - log(2)/3.
Sum_{n>=4} (-1)^n/a(n) = 9*log(3/2) - 65/18. (End)
MAPLE
spec := [S, {B=Set(Z), S=Prod(Z, Z, Z, Z, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
Range[0, 30]!* CoefficientList[Series[Exp[x]^2 * x^4, {x, 0, 30}], x] (* Vincenzo Librandi, Dec 06 2012 *)
PROG
(Magma) [(n-3)*(n-2)*(n-1)*n * 2^(n-4): n in [0..30]]; // Vincenzo Librandi, Dec 06 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from Vincenzo Librandi, Dec 06 2012
STATUS
approved