OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..800
FORMULA
E.g.f.: (2*exp(x^2/2)*x+2+sqrt(2*Pi)*exp(x^2/2)*erf(x/sqrt(2))*x) / (2*exp(x)).
a(n) = (n-2)*a(n-3)+(n-1)*a(n-2)-2*a(n-1) for n>2, a(n) = (n-1)^2 otherwise.
a(n) = Sum_{k=0..n} (-1)^k * C(n,k) * A006882(n-k).
a(n) ~ (-1)^n * (sqrt(Pi) - sqrt(2)) * exp(sqrt(n) - n/2 - 1/4) * n^((n+1)/2) / 2. - Vaclav Kotesovec, Oct 31 2017
G.f.: Sum_{k>=0} k!!*x^k/(1 + x)^(k+1). - Ilya Gutkovskiy, Apr 12 2019
MAPLE
a:= proc(n) option remember; `if`(n<3, (n-1)^2,
(n-2)*a(n-3) +(n-1)*a(n-2) -2*a(n-1))
end:
seq(a(n), n=0..30);
MATHEMATICA
Table[Sum[(-1)^(n-k) * Binomial[n, k] * k!!, {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 31 2017 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Alois P. Heinz, Oct 22 2015
STATUS
approved