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

%I A052796 #33 Mar 15 2023 11:04:48
%S A052796 0,0,0,0,24,240,1440,6720,26880,96768,322560,1013760,3041280,8785920,
%T A052796 24600576,67092480,178913280,467927040,1203240960,3048210432,
%U A052796 7620526080,18827182080,46022000640,111421685760,267412045824,636695347200,1504916275200
%N A052796 Expansion of e.g.f. x^4*exp(x)^2.
%C A052796 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.
%H A052796 Vincenzo Librandi, <a href="/A052796/b052796.txt">Table of n, a(n) for n = 0..1000</a>
%H A052796 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=753">Encyclopedia of Combinatorial Structures 753</a>.
%F A052796 E.g.f.: x^4*exp(x)^2.
%F A052796 a(n) = A090802(n, 4).
%F A052796 Recurrence: {a(1)=0, a(2)=0, a(3)=0, a(4)=24, (-2*n-2)*a(n)+(n-3)*a(n+1)}.
%F A052796 O.g.f.: -24*x^4/(2*x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009
%F A052796 a(n) = (n-3)*(n-2)*(n-1)*n * 2^(n-4). - _Vaclav Kotesovec_, Nov 27 2012
%F A052796 From _Amiram Eldar_, Jan 09 2022: (Start)
%F A052796 Sum_{n>=4} 1/a(n) = 5/18 - log(2)/3.
%F A052796 Sum_{n>=4} (-1)^n/a(n) = 9*log(3/2) - 65/18. (End)
%p A052796 spec := [S,{B=Set(Z),S=Prod(Z,Z,Z,Z,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052796 Range[0, 30]!* CoefficientList[Series[Exp[x]^2 * x^4,{x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 06 2012 *)
%o A052796 (Magma) [(n-3)*(n-2)*(n-1)*n * 2^(n-4): n in [0..30]]; // _Vincenzo Librandi_, Dec 06 2012
%Y A052796 Cf. A090802.
%K A052796 easy,nonn
%O A052796 0,5
%A A052796 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052796 More terms from _Vincenzo Librandi_, Dec 06 2012