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A056543
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a(n) = n*a(n-1) - 1 with a(1)=1.
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2
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1, 1, 2, 7, 34, 203, 1420, 11359, 102230, 1022299, 11245288, 134943455, 1754264914, 24559708795, 368395631924, 5894330110783, 100203611883310, 1803665013899579, 34269635264092000, 685392705281839999
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| If s(n) is a sequence defined by s(0)=x, s(n)=(n+1)*s(n-1)+k,n>0 then s(n) = n!*x +(n!-a(n+1))*k [From Gary Detlefs (gdetlefs(AT)aol.com), Jun 10 2010]
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FORMULA
| a(n) =ceiling[(3-e)*n! ] =n!-A056542(n) =2*n!-A002627(n) =3*n!-A000522(n)
a(n)=n!*[2-Sum_{k=1..n}{k!^(-1)}], with n>=1 [From Paolo P. Lava (paoloplava(AT)gmail.com), Jun 25 2010]
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EXAMPLE
| a(4)=4*a(3)-1=4*2-1=7
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MATHEMATICA
| lst={1}; s=-1; Do[s+=s++n; AppendTo[lst, Abs[s]], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 23 2008]
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CROSSREFS
| Sequence in context: A199475 A117399 A145345 * A075834 A011800 A112916
Adjacent sequences: A056540 A056541 A056542 * A056544 A056545 A056546
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KEYWORD
| easy,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 20 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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