OFFSET
6,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 6..200
FindStat - Combinatorial Statistic Finder, The number of fixed points of a permutation
FORMULA
a(n) = A008290(n,6).
E.g.f.: exp(-x)/(1-x)*(x^6/6!). [Zerinvary Lajos, Apr 03 2009]
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
MAPLE
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
MATHEMATICA
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 *)
PROG
(PARI) x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^6/6!)) ) \\ Joerg Arndt, Feb 19 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Zerinvary Lajos, May 25 2007
EXTENSIONS
Changed offset from 0 to 6 by Vincenzo Librandi, Feb 19 2014
Edited by Joerg Arndt, Feb 19 2014
STATUS
approved