A052779 Expansion of e.g.f.: (log(1-x))^6.

0, 0, 0, 0, 0, 0, 720, 15120, 231840, 3265920, 45556560, 649479600, 9604465200, 148370508000, 2402005525920, 40797624067200, 726963917097600, 13580328282393600, 265689107448756480, 5437099866285377280, 116229410301685651200, 2591985252922277184000, 60218914823672258142720

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

Original name: a simple grammar.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 736

Crossrefs

Column k=6 of A225479.

Cf. A001233, A052517.

Programs

Maple

spec := [S,{B=Cycle(Z),S=Prod(B,B,B,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

PARI

a(n) = {6!*stirling(n,6,1)*(-1)^n} \\ Andrew Howroyd, Jul 27 2020

Formula

E.g.f.: log(-1/(-1+x))^6.

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)}.

a(n) = 720*A001233(n) = 6!*(-1)^n*Stirling1(n,6). - Andrew Howroyd, Jul 27 2020

Extensions

Name changed and terms a(20) and beyond from Andrew Howroyd, Jul 27 2020