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A129149
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Permutations with exactly 7 fixed points.
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3
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1, 0, 36, 240, 2970, 34848, 454740, 6362928, 95450355, 1527194240, 25962321528, 467321755680, 8879113408308, 177582268088640, 3729227629977720, 82043007859339296, 1886989180765048965, 45287740338360829056
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OFFSET
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7,3
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LINKS
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FORMULA
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Conjecture: (-n+7)*a(n) +n*(n-8)*a(n-1) +n*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 02 2015
O.g.f.: (1/7!)*Sum_{k>=7} k!*x^k/(1 + x)^(k+1). - Ilya Gutkovskiy, Apr 15 2017
D-finite with recurrence (-n+7)*a(n) +n*(n-8)*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-6)!, j=0..n), k=6..n): seq(a(n)/7!, n=6..24);
restart: G(x):=exp(-x)/(1-x)*(x^7/7!): 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=7..24); # 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^7/7!, {x, 0, nn}], x]Range[0, nn]!, 7]] (* 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^7/7!)) ) \\ 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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