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A030297
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a(n) = n*(n+a(n-1)).
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6
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0, 1, 6, 27, 124, 645, 3906, 27391, 219192, 1972809, 19728190, 217010211, 2604122676, 33853594957, 473950329594, 7109254944135, 113748079106416, 1933717344809361, 34806912206568822, 661331331924807979
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| For n>=2, a(n) = floor(2*e*n!-n-2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 16 2003
a(n) = Sum[(n! / k!) * k^2 {k=0...n}] - Ross La Haye (rlahaye(AT)new.rr.com), Sep 21 2004
E.g.f.: x*(1+x)*exp(x)/(1-x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 01 2004
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MAPLE
| f := proc(n) options remember; if n <= 1 then n elif n = 2 then 6 else -n*(n-2)*f(n-3)+(n-3)*n*f(n-2)+3*n*f(n-1)/(n-1); fi; end;
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MATHEMATICA
| a=0; lst={a}; Do[a=(a+n)*n; AppendTo[lst, a], {n, 2*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 14 2008]
RecurrenceTable[{a[0]==0, a[n]==n(n+a[n-1])}, a[n], {n, 20}] (* From Harvey P. Dale, Oct 22 2011 *)
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CROSSREFS
| a(n) = A019461(2n). Cf. A019462-A019464.
Cf. A006183, A054096.
Sequence in context: A175716 A178935 A002912 * A045500 A109115 A038176
Adjacent sequences: A030294 A030295 A030296 * A030298 A030299 A030300
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), "Urkonsaud_admin" (miti(AT)tula.sitek.net)
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EXTENSIONS
| Better description from Henry Bottomley (se16(AT)btinternet.com), May 15 2000
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