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

0, 0, 0, 0, 0, 0, 720, 7560, 70560, 680400, 7015680, 78004080, 935542080, 12074119200, 167122859904, 2472036446880, 38940240568320, 651087633530880, 11519998092877824, 215088381671892480, 4226801728115404800, 87218325048627763200, 1885639117481531596800

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 743

Crossrefs

Cf. A052765, A052766.

Programs

Maple

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

PARI

a(n)={if(n>=3, 3!*n*(n-1)*(n-2)*abs(stirling(n-3,3,1)), 0)} \\ Andrew Howroyd, Aug 08 2020

Formula

E.g.f.: x^3*log(-1/(-1+x))^3.

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)}.

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

Extensions

Named changed and terms a(20) and beyond from Andrew Howroyd, Aug 08 2020