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A070947
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Number of permutations on n letters that have only cycles of length 6 or less.
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5
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1, 1, 2, 6, 24, 120, 720, 4320, 29520, 225360, 1890720, 17169120, 166112640, 1680462720, 18189031680, 209008512000, 2532028896000, 32143053484800, 425585741760000, 5865854258188800, 84489178710067200, 1266667808011315200, 19700712491727974400
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OFFSET
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0,3
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LINKS
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FORMULA
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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).
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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