OFFSET
0,4
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
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
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
PROG
(PARI) a(n) = {3!*stirling(n, 3, 1)*(-1)^(n+1)} \\ Andrew Howroyd, Jul 27 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
Name changed and terms a(20) and beyond from Andrew Howroyd, Jul 27 2020
STATUS
approved