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A129136
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Permutations with exactly 6 fixed points.
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3
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1, 0, 28, 168, 1890, 20328, 244860, 3181464, 44543499, 668147480, 10690367688, 181736238320, 3271252308324, 62153793831024, 1243075876659240, 26104593409789776, 574301055015449685, 13208924265355241808
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OFFSET
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6,3
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LINKS
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FORMULA
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O.g.f.: (1/6!)*Sum_{k>=6} k!*x^k/(1 + x)^(k+1). - Ilya Gutkovskiy, Apr 15 2017
D-finite with recurrence +(-n+6)*a(n) +n*(n-7)*a(n-1) +n*(n-1)*a(n-2)=0. - R. J. Mathar, Jul 06 2023
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MAPLE
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a:=n->sum(n!*sum((-1)^k/(k-5)!, j=0..n), k=5..n): seq(-a(n)/6!, n=5..24);
restart: G(x):=exp(-x)/(1-x)*(x^6/6!): 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=6..23); # 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^6/6!, {x, 0, nn}], x]Range[0, nn]!, 6]] (* 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^6/6!)) ) \\ 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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