OFFSET
0,3
FORMULA
E.g.f.: Sum_{k>=0} (k * x)^k / (k! * (1 - (k * x)^2)).
MAPLE
f:= proc(n) local k; n! * add((n-2*k)^n/(n-2*k)!, k=0..floor(n/2)) end proc:
map(f, [$0..20]); # Robert Israel, Sep 16 2022
MATHEMATICA
a[n_] := n! * Sum[(n - 2*k)^n/(n - 2*k)!, {k, 0, Floor[n/2]} ]; a[0] = 1; Array[a, 18, 0] (* Amiram Eldar, Sep 16 2022 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^n/(n-2*k)!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x)^k/(k!*(1-(k*x)^2)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 16 2022
STATUS
approved