This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A357191 #9 Sep 17 2022 08:44:53
%S A357191 1,0,2,6,216,2040,111240,2164680,159391680,5247305280,491431600800,
%T A357191 24437592194400,2800955712804480,195393943295591040,
%U A357191 26699221909806526080,2479967110139382864000,396503602252401676032000,47167550656581451928832000
%N A357191 a(n) = n! * Sum_{k=0..floor(n/2)} k^n/k!.
%F A357191 E.g.f.: Sum_{k>=0} (k * x)^(2 * k) / (k! * (1 - k * x)).
%o A357191 (PARI) a(n) = n!*sum(k=0, n\2, k^n/k!);
%o A357191 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x)^(2*k)/(k!*(1-k*x)))))
%Y A357191 Cf. A256016, A357192.
%Y A357191 Cf. A352981, A357193.
%K A357191 nonn
%O A357191 0,3
%A A357191 _Seiichi Manyama_, Sep 17 2022