OFFSET
0,3
REFERENCES
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
Alois P. Heinz, Table of n, a(n) for n = 0..450 (terms n = 1..100 from T. D. Noe)
J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
FORMULA
Nearest integer to n!(1+1/e).
a(n) = A000166(n) + [n > 0] * n!. - Philippe Del�ham, Sep 04 2005
a(n) = (n-1)*(a(n-1)+a(n-2)), n>2. - Gary Detlefs, Apr 11 2010
E.g.f.: (exp(x)*x+1)*exp(-x)/(1-x). - Alois P. Heinz, May 08 2020
MAPLE
a:= proc(n) option remember;
`if`(n<2, 1, n*a(n-1)+(-1)^n)
end:
seq(a(n), n=0..23); # Alois P. Heinz, May 09 2020
MATHEMATICA
t = {1}; Do[AppendTo[t, n*t[[-1]] + (-1)^n], {n, 2, 20}]; t (* T. D. Noe, Jun 26 2012 *)
RecurrenceTable[{a[1]==1, a[n]==n a[n-1]+(-1)^n}, a, {n, 30}] (* Harvey P. Dale, Feb 19 2018 *)
PROG
(PARI) a(n)=if(n<2, n>0, n*a(n-1)+(-1)^n)
(PARI) a(n)=if(n<1, 0, n!*polcoeff((1+exp(-x+x*O(x^n)))/(1-x), n))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, May 08 2020
STATUS
approved