|
%I #17 Jul 27 2020 16:47:52
%S 0,0,0,0,0,0,720,15120,231840,3265920,45556560,649479600,9604465200,
%T 148370508000,2402005525920,40797624067200,726963917097600,
%U 13580328282393600,265689107448756480,5437099866285377280,116229410301685651200,2591985252922277184000,60218914823672258142720
%N Expansion of e.g.f.: (log(1-x))^6.
%C Original name: a simple grammar.
%H Andrew Howroyd, <a href="/A052779/b052779.txt">Table of n, a(n) for n = 0..200</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=736">Encyclopedia of Combinatorial Structures 736</a>
%F E.g.f.: log(-1/(-1+x))^6.
%F Recurrence: {a(1)=0, a(0)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (1+15*n^2+6*n+6*n^5+15*n^4+20*n^3+n^6)*a(n+1) + (-63-186*n-225*n^2-6*n^5-45*n^4-140*n^3)*a(n+2) + (540*n+120*n^3+375*n^2+15*n^4+301)*a(n+3) + (-390*n-20*n^3-350-150*n^2)*a(n+4) + (140+15*n^2+90*n)*a(n+5) + (-21-6*n)*a(n+6) + a(n+7)}.
%F a(n) = 720*A001233(n) = 6!*(-1)^n*Stirling1(n,6). - _Andrew Howroyd_, Jul 27 2020
%p spec := [S,{B=Cycle(Z),S=Prod(B,B,B,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%o (PARI) a(n) = {6!*stirling(n,6,1)*(-1)^n} \\ _Andrew Howroyd_, Jul 27 2020
%Y Column k=6 of A225479.
%Y Cf. A001233, A052517.
%K easy,nonn
%O 0,7
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E Name changed and terms a(20) and beyond from _Andrew Howroyd_, Jul 27 2020
|
