A052748 Expansion of e.g.f.: -(log(1-x))^3.

0, 0, 0, 6, 36, 210, 1350, 9744, 78792, 708744, 7036200, 76521456, 905507856, 11589357312, 159580302336, 2352940786944, 36994905688320, 617953469022720, 10929614667747840, 204073497562936320, 4011658382046919680, 82822558521844224000, 1791791417179298304000

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 704

Crossrefs

Column k=3 of A225479.

Cf. A000399, A052517.

Programs

Maple

spec := [S,{B=Cycle(Z),S=Prod(B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
with(combinat):seq(stirling1(j, 3)*3!*(-1)^(j+1), j=0..50); # Leonid Bedratyuk, Aug 07 2012

PARI

a(n) = {3!*stirling(n,3,1)*(-1)^(n+1)} \\ Andrew Howroyd, Jul 27 2020

Formula

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

Recurrence: {a(1)=0, a(0)=0, a(2)=0, a(3)=6, (-1 - 3*n - 3*n^2 - n^3)*a(n+1) + (9*n + 7 + 3*n^2)*a(n+2) + (-6 - 3*n)*a(n+3) + a(n+4)}.

a(n) = stirling1(n, 3)*3!*(-1)^(n+1). - Leonid Bedratyuk, Aug 07 2012

a(n) = 6*A000399(n). - Andrew Howroyd, Jul 27 2020

Extensions

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