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A070946
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Number of permutations on n letters that have only cycles of length 5 or less.
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1
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1, 1, 2, 6, 24, 120, 600, 3480, 22800, 164880, 1285920, 10516320, 92931840, 877374720, 8762014080, 91819440000, 1005716908800, 11584953158400, 139521689740800, 1748830512960000, 22750446292531200, 306931140411955200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Vladimir Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565
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FORMULA
| E.g.f.: exp(x+1/2*x^2+1/3*x^3+1/4*x^4+1/5*x^5).
a(n)=n!*sum(k=1..n, 1/k!*sum(r=0..k, binomial(k,r)*sum(m=0..r, 2^(m-r)*binomial(r,m)*sum(j=0..m, binomial(m,j)*binomial(j,n-m-k-j-r)*3^(j-m)*4^(n-r-m-k-2*j)*5^(m+k+j+r-n))))
[From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Jan 26 2011]
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MAPLE
| with (combstruct):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, m>=card))}, labeled]; end: A:=a(5):seq(count(A, size=n), n=0..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008
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CROSSREFS
| Cf. A057693.
Sequence in context: A179351 A179357 A179364 * A060726 A152332 A152349
Adjacent sequences: A070943 A070944 A070945 * A070947 A070948 A070949
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and Sharon Sela, May 18 2002
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