%I #9 Sep 17 2022 08:44:53
%S 1,0,2,6,216,2040,111240,2164680,159391680,5247305280,491431600800,
%T 24437592194400,2800955712804480,195393943295591040,
%U 26699221909806526080,2479967110139382864000,396503602252401676032000,47167550656581451928832000
%N a(n) = n! * Sum_{k=0..floor(n/2)} k^n/k!.
%F E.g.f.: Sum_{k>=0} (k * x)^(2 * k) / (k! * (1 - k * x)).
%o (PARI) a(n) = n!*sum(k=0, n\2, k^n/k!);
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x)^(2*k)/(k!*(1-k*x)))))
%Y Cf. A256016, A357192.
%Y Cf. A352981, A357193.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 17 2022