OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..514
P. L. Krapivsky, J. M. Luck, Coverage fluctuations in theater models, arXiv:1902.04365 [cond-mat.stat-mech], 2019.
R. Petuchovas, Asymptotic analysis of the cyclic structure of permutations, arXiv:1611.02934 [math.CO], p. 6, 2016.
FORMULA
E.g.f.: exp(x+1/2*x^2+1/3*x^3+1/4*x^4+1/5*x^5+1/6*x^6).
MAPLE
with(combstruct):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, m>=card))}, labeled]; end: A:=a(6):seq(count(A, size=n), n=0..21); # Zerinvary Lajos, Jun 11 2008
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
*binomial(n-1, j-1)*(j-1)!, j=1..min(n, 6)))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Dec 28 2017
MATHEMATICA
terms = 22; CoefficientList[Exp[-Log[1-x] + O[x]^7 // Normal] + O[x]^terms, x]*Range[0, terms-1]! (* Jean-François Alcover, Dec 28 2017 *)
PROG
(Python)
from sympy.core.cache import cacheit
from sympy import binomial, factorial as f
@cacheit
def a(n): return 1 if n==0 else sum(a(n-j)*binomial(n - 1, j - 1)*f(j - 1) for j in range(1, min(n, 6)+1))
print([a(n) for n in range(31)]) # Indranil Ghosh, Dec 29 2017, after Alois P. Heinz
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane and Sharon Sela, May 18 2002
STATUS
approved