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Search: id:A082491
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| A082491 |
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a(n) = n! d(n), where n! = factorial numbers (A000142), d(n) = subfactorial numbers (A000166). |
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1
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| 1, 0, 2, 12, 216, 5280, 190800, 9344160, 598066560, 48443028480, 4844306476800, 586161043776000, 84407190782745600, 14264815236056985600, 2795903786354347468800, 629078351928420506112000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) is also the number of pairs of n-permutations p and q such that p(x)<>q(x) for each x in { 1, 2, ..., n }.
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LINKS
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Ira Gessel, Enumerative applications of symmetric functions
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FORMULA
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Formula: Sum[ binomial[n, k]^2 (-1)^k (n - k)!^2 k!, {k, 0, n} ] = n! d(n) Recurrence: a(n+2) = (n+2)(n+1) ( a(n+1) + (n+1) a(n) )
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MAPLE
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with (combstruct):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, card>=m))}, labeled]; end: ZLL:=a(2):seq(count(ZLL, size=n)*n!, n=0..15); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008
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CROSSREFS
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Cf. A000142, A000166.
Adjacent sequences: A082488 A082489 A082490 this_sequence A082492 A082493 A082494
Sequence in context: A012598 A129893 A008352 this_sequence A123118 A083667 A092124
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KEYWORD
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easy,nonn
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AUTHOR
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Emanuele Munarini (munarini(AT)mate.polimi.it), Apr 28 2003
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