cp's OEIS Frontend

A052786 Expansion of e.g.f.: -x^3*(log(1-x))^3.

%I A052786 #15 Aug 08 2020 16:08:45
%S A052786 0,0,0,0,0,0,720,7560,70560,680400,7015680,78004080,935542080,
%T A052786 12074119200,167122859904,2472036446880,38940240568320,
%U A052786 651087633530880,11519998092877824,215088381671892480,4226801728115404800,87218325048627763200,1885639117481531596800
%N A052786 Expansion of e.g.f.: -x^3*(log(1-x))^3.
%C A052786 Original name: a simple grammar.
%H A052786 Andrew Howroyd, <a href="/A052786/b052786.txt">Table of n, a(n) for n = 0..200</a>
%H A052786 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=743">Encyclopedia of Combinatorial Structures 743</a>
%F A052786 E.g.f.: x^3*log(-1/(-1+x))^3.
%F A052786 Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (16*n^4+135*n+162-81*n^2-42*n^3-n^6+3*n^5)*a(n) + (-228+81*n^2+3*n^5+104*n-38*n^3-6*n^4)*a(n+1) + (36+6*n^3-3*n^4+21*n^2-60*n)*a(n+2) + (-3*n^2+n^3+2*n)*a(n+3)}.
%F A052786 a(n) = n*A052765(n-1) = 3!*n*(n-1)*(n-2)*abs(Stirling1(n-3,3)) for n >= 3. - _Andrew Howroyd_, Aug 08 2020
%p A052786 spec := [S,{B=Cycle(Z),S=Prod(Z,Z,Z,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%o A052786 (PARI) a(n)={if(n>=3, 3!*n*(n-1)*(n-2)*abs(stirling(n-3,3,1)), 0)} \\ _Andrew Howroyd_, Aug 08 2020
%Y A052786 Cf. A052765, A052766.
%K A052786 easy,nonn
%O A052786 0,7
%A A052786 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052786 Named changed and terms a(20) and beyond from _Andrew Howroyd_, Aug 08 2020