OFFSET
7,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 7..200
P. Barry and A. Hennessy, Four-term Recurrences, Orthogonal Polynomials and Riordan Arrays, Journal of Integer Sequences, 2012, article 12.4.2. - From N. J. A. Sloane, Sep 21 2012
FORMULA
a(n) = A008290(n,7).
E.g.f.: exp(-x)/(1-x)*(x^7/7!). [Zerinvary Lajos, Apr 03 2009]
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
MAPLE
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
MATHEMATICA
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 *)
PROG
(PARI) x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^7/7!)) ) \\ Joerg Arndt, Feb 19 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Zerinvary Lajos, May 25 2007
EXTENSIONS
Changed offset from 0 to 7 by Vincenzo Librandi, Feb 19 2014
Edited by Joerg Arndt, Feb 19 2014
STATUS
approved