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A052790 Expansion of e.g.f.: x^2*log(1-x)^4.

%I A052790 #17 Aug 08 2020 16:08:53
%S A052790 0,0,0,0,0,0,720,10080,114240,1270080,14621040,177629760,2292618240,
%T A052790 31485168000,459767275968,7126635035520,117007217832960,
%U A052790 2030137891891200,37138576448883456,714734162773420032,14439823458634690560,305638240397811793920,6764967047810572812288
%N A052790 Expansion of e.g.f.: x^2*log(1-x)^4.
%C A052790 Original name: a simple grammar.
%H A052790 Andrew Howroyd, <a href="/A052790/b052790.txt">Table of n, a(n) for n = 0..200</a>
%H A052790 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=747">Encyclopedia of Combinatorial Structures 747</a>
%F A052790 E.g.f.: x^2*log(-1/(-1+x))^4.
%F A052790 Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (32*n-464*n^2-21*n^6-22*n^5+48*n^3+n^8+2*n^7+384+160*n^4)*a(n) + (105*n^4-360-14*n^6-121*n^2-4*n^7+642*n-296*n^3+48*n^5)*a(n+1) + (-84*n+24*n^5+179*n^2+6*n^6-35*n^4-90*n^3)*a(n+2) + (14*n^2+12*n^3-8*n-14*n^4-4*n^5)*a(n+3) + (-n^2+n^4-2*n+2*n^3)*a(n+4)}.
%F A052790 a(n) = n*A052770(n-1) = 4!*n*(n-1)*abs(Stirling1(n-2,4)) for n >= 2. - _Andrew Howroyd_, Aug 08 2020
%p A052790 spec := [S,{B=Cycle(Z),S=Prod(Z,Z,B,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052790 With[{nn=20},CoefficientList[Series[x^2 Log[-1/(x-1)]^4,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 28 2016 *)
%o A052790 (PARI) a(n)={if(n>=2, 4!*n*(n-1)*abs(stirling(n-2,4,1)), 0)} \\ _Andrew Howroyd_, Aug 08 2020
%Y A052790 Cf. A052754, A052770.
%K A052790 easy,nonn
%O A052790 0,7
%A A052790 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052790 Name changed and terms a(20) and beyond from _Andrew Howroyd_, Aug 08 2020