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A086325
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Let u(1)=0, u(2)=1, u(k)=u(k-1)+u(k-2)/(k-2); then a(n)=n!*u(n).
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0, 2, 6, 36, 220, 1590, 12978, 118664, 1201464, 13349610, 161530270, 2114578092, 29780308116, 448995414686, 7215997736010, 123153028027920, 2224451568754288, 42395429898611154, 850263899633257014
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n) = ceiling(n*n!/e) - (1-(-1)^n)/2.
E.g.f.: x^2*exp(-x)/(1-x)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 20 2003
a(n) = n*floor((n!+1)/e) [From Gary Detlefs (gdetlefs(AT)aol.com), Jul 13 2010]
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MAPLE
| a:=n->sum((n+1)!*sum((-1)^k/k!, j=1..n-k), k=0..n): seq(a(n), n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2007
a:=n->n!*sum((-1)^k/k!, k=0..n): seq(a(n)*n, n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 18 2007
with (combstruct):with (combinat):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, card>=m))}, labeled]; end: ZLL:=a(2):seq(count(ZLL, size=n)*fibonacci(2, n), n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008
with (combstruct):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, card>=m))}, labeled]; end: ZLL:=a(2):seq(count(ZLL, size=n)*n, n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008
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MATHEMATICA
| Table[Subfactorial[n]*n, {n, 1, 19}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 09 2009]
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CROSSREFS
| Cf. A000246.
Cf. A000274.
Cf. A000166.
Sequence in context: A019020 A101609 A152668 * A074424 A002868 A002869
Adjacent sequences: A086322 A086323 A086324 * A086326 A086327 A086328
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 30 2003
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