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A129217
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Permutations with exactly 9 fixed points.
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3
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1, 0, 55, 440, 6435, 88088, 1326325, 21209760, 360590230, 6490575520, 123321027258, 2466420377200, 51794828215130, 1139486220235440, 26208183066232310, 628996393588267936, 15724909839708741375
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OFFSET
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9,3
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LINKS
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FORMULA
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O.g.f.: (1/9!)*Sum_{k>=9} k!*x^k/(1 + x)^(k+1). - Ilya Gutkovskiy, Apr 15 2017
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MAPLE
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a:=n->sum(n!*sum((-1)^k/(k-8)!, j=0..n), k=8..n): seq(a(n)/9!, n=8..27);
restart: G(x):=exp(-x)/(1-x)*(x^9/9!): f[0]:=G(x): for n from 1 to 26 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=9..25); # Zerinvary Lajos, Apr 03 2009
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MATHEMATICA
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With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^9/9!, {x, 0, nn}], x]Range[0, nn]!, 9]] (* Vincenzo Librandi, Feb 19 2014 *)
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PROG
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(PARI) x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^9/9!)) ) \\ Joerg Arndt, Feb 19 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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