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A052761 a(n) = 3!*n*S(n-1,3), where S denotes the Stirling numbers of second kind.

%I A052761 #27 Aug 09 2020 17:16:09
%S A052761 0,0,0,0,24,180,900,3780,14448,52164,181500,615780,2052072,6749028,
%T A052761 21976500,71007300,228009696,728451972,2317445100,7346047140,
%U A052761 23213772120,73156412196,229989358500,721474964100,2258832312144,7059480120900,22026886599900
%N A052761 a(n) = 3!*n*S(n-1,3), where S denotes the Stirling numbers of second kind.
%H A052761 Matthew House, <a href="/A052761/b052761.txt">Table of n, a(n) for n = 0..2079</a>
%H A052761 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=718">Encyclopedia of Combinatorial Structures 718</a>
%H A052761 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (12,-58,144,-193,132,-36).
%F A052761 E.g.f.: exp(x)^3*x - 3*exp(x)^2*x + 3*x*exp(x) - x.
%F A052761 Recurrence: {a(1)=0, a(2)=0, a(3)=0, a(4)=24, (-36*n^2 - 66*n - 6*n^3 - 36)*a(n) + (11*n^3 + 55*n^2 + 66*n)*a(n+1) + (-6*n^3 - 24*n^2 - 18*n)*a(n+2) + (n^3 + 3*n^2 + 2*n)*a(n+3)}
%F A052761 For n>=2, a(n) = n*(3^(n-1) - 3*2^(n-1) + 3). - _Vaclav Kotesovec_, Nov 27 2012
%F A052761 O.g.f.: 12*x^4*(2 - 9*x + 11*x^2 - 3*x^3)/((1 - 3*x)^2*(1 - 2*x)^2*(1 - x)^2). - _Matthew House_, Feb 16 2017 [Corrected by _Georg Fischer_, May 19 2019]
%F A052761 From _Andrew Howroyd_, Aug 08 2020: (Start)
%F A052761 a(n) = n*A001117(n-1) for n > 1.
%F A052761 E.g.f.: x*(exp(x) - 1)^3. (End)
%p A052761 spec := [S,{B=Set(Z,1 <= card),S=Prod(B,B,B,Z)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052761 Join[{0},Table[3!*n*StirlingS2[n-1,3],{n,30}]] (* _Harvey P. Dale_, Feb 07 2015 *)
%o A052761 (PARI) a(n)={if(n>=1, 3!*n*stirling(n-1, 3, 2), 0)} \\ _Andrew Howroyd_, Aug 08 2020
%Y A052761 Cf. A000392, A001117, A052749.
%K A052761 nonn,easy
%O A052761 0,5
%A A052761 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052761 Better description from Victor Adamchik (adamchik(AT)cs.cmu.edu), Jul 19 2001
%E A052761 More terms from _Harvey P. Dale_, Feb 07 2015