OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..450
FORMULA
From Vladeta Jovovic, Jul 16 2007: (Start)
G.f.: x/(1+x)*Sum_{n>=0} (n+1)!*(x/(1+x)^2)^n.
a(n) = Sum_{k=1..n} (-1)^(n-k)*k!*binomial(n+k-2,2*k-2). (End)
a(n) ~ exp(-2) * n!. - Vaclav Kotesovec, Aug 25 2014
MAPLE
a:= proc(n) option remember; `if`(n<4, 1,
(n-1)*a(n-1) +(n-3)*a(n-2) +a(n-3))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Jan 10 2014
MATHEMATICA
a = DifferenceRoot[Function[{y, n}, {-y[n] - n y[n+1] - (n+2) y[n+2] + y[n+3] == 0, y[0] == 1, y[1] == 1, y[2] == 1, y[3] == 1}]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Baltic, Vladeta Jovovic, Jan 05 2003
EXTENSIONS
More terms from Alois P. Heinz, Jan 10 2014
STATUS
approved