A052796 Expansion of e.g.f. x^4*exp(x)^2.

0, 0, 0, 0, 24, 240, 1440, 6720, 26880, 96768, 322560, 1013760, 3041280, 8785920, 24600576, 67092480, 178913280, 467927040, 1203240960, 3048210432, 7620526080, 18827182080, 46022000640, 111421685760, 267412045824, 636695347200, 1504916275200

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

Cf. A090802.

Sequence in context: A167548 A192849 A253285 * A056269 A000919 A353665

Adjacent sequences: A052793 A052794 A052795 * A052797 A052798 A052799

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

More terms from Vincenzo Librandi, Dec 06 2012

Status

approved