OFFSET
0,2
REFERENCES
Herbert S. Wilf, Generatingfunctiontology, page 209
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..150
H. Crane and P. McCullagh, Reversible Markov structures on divisible set partitions, Journal of Applied Probability, 52(3), 2015.
FORMULA
a(n) = (-1)^(n/3)*binomial(-1/3,n/3)*n!.
E.g.f.: 1/(1-x^3)^(1/3).
a(n) = ((3*n)!/(n!*3^n))*Product_{i=1..n-1} (1+3*i) (from the Wilf reference).
a(n) ~ (3*n)! / (Gamma(1/3) * n^(2/3)). - Vaclav Kotesovec, Jun 15 2015
D-finite with recurrence: a(n) = (3*n-1)*(3*n-2)^2*a(n-1), a(0)=1. - Georg Fischer, Jul 02 2021 (from the 3rd formula)
EXAMPLE
a(1) = 2 because we have (123) and (132).
MAPLE
a:= n-> factorial(3*n)*(mul(1+3*i, i = 1 .. n-1))/(factorial(n)*3^n): seq(a(n), n = 0 .. 11);
MATHEMATICA
Table[(-1)^(n/3) Binomial[-1/3, n/3]n!, {n, 0, 30, 3}]
PROG
(PARI) v=Vec(serlaplace(1/(1-x^3+O(x^50))^(1/3))); vector(#v\3, n, v[3*n-2])
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Dec 23 2010
STATUS
approved