OFFSET
0,4
COMMENTS
a(n) is the number of labeled sequences of cycles, where no cycle has size 1.
REFERENCES
P. Flajolet and R. Segdewick, Analytic Combinatorics, Cambridge University Press, 2009, page 119
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: 1/(1+x-log(1/(1-x)))
a(n) ~ n!*c/(1-c)^(n+2), where c = -LambertW(-exp(-2)) = 0.158594339563... - Vaclav Kotesovec, Jun 02 2013
a(0) = 1; a(n) = Sum_{k=0..n-2} binomial(n,k) * (n-k-1)! * a(k). - Ilya Gutkovskiy, Apr 26 2021
EXAMPLE
For n=4, the a(4)=12 alignments with no singletons are: 1234, 1243, 1324, 1342, 1423, 1432, 12|34, 13|24, 14|23, 23|14, 24|13, 34|12.
MATHEMATICA
Range[0, 50]! CoefficientList[ Series[(1 + z - Log[1/(1 - z)])^(-1), {z, 0, 50}], z]
PROG
(PARI) x='x+O('x^66); Vec(serlaplace(1/(1+x-log(1/(1-x))))) \\ Joerg Arndt, Jun 01 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Ricardo Bittencourt, May 31 2013
STATUS
approved