OFFSET
1,6
REFERENCES
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
FORMULA
(n-1)*a(n) = (n+3)*(a(n-1)*n + a(n-2)*n - a(n-1) + 2*a(n-2)).
E.g.f.: (for offset 4): (x^4/4!)*exp(-x)/(1-x)^2. - Vladeta Jovovic, Jan 03 2003
G.f.: (for offset 0): hypergeom([2, 5],[],x/(x+1))/(x+1)^5. - Mark van Hoeij, Nov 07 2011
Recurrence (for offset 5): (n-5)*a(n) = (n-5)*(n-1)*a(n-1) + (n-2)*(n-1)*a(n-2). - Vaclav Kotesovec, Mar 26 2014
a(n) ~ n! * exp(-1)/24. - Vaclav Kotesovec, Mar 26 2014
MAPLE
a:=n->sum((n+2)!*sum((-1)^k/k!/4!, j=1..n), k=0..n): seq(a(n), n=2..19); # Zerinvary Lajos, May 25 2007
series(hypergeom([2, 5], [], x/(x+1))/(x+1)^5, x=0, 30); # Mark van Hoeij, Nov 07 2011
MATHEMATICA
Drop[CoefficientList[Series[x^4/4! Exp[-x]/(1 - x)^2, {x, 0, 20}], x] Range[0, 20]!, 4] (* Vaclav Kotesovec, Mar 26 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Jan 03 2003
Name clarified and offset changed by N. J. A. Sloane, Apr 12 2014
STATUS
approved