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 A345747 #59 Oct 30 2022 08:58:37
%S A345747 1,0,2,6,36,240,2280,27720,425040,7862400,171188640,4319330400,
%T A345747 125199708480,4142318019840,155388782989440,6557345831836800,
%U A345747 308677784640825600,16079233115648102400,920518264903690252800,57603377545940850624000
%N A345747 a(n) = n! * Sum_{k=0..floor(n/2)} k^(n - 2*k)/k!.
%H A345747 Seiichi Manyama, <a href="/A345747/b345747.txt">Table of n, a(n) for n = 0..315</a>
%F A345747 E.g.f.: Sum_{k>=0} x^(2*k) / (k! * (1 - k * x)).
%F A345747 a(n) ~ sqrt(2*Pi) * exp((n - 1/2)/LambertW(exp(2/3)*(2*n - 1)/6) - 2*n) * n^(2*n + 1/2) / (3^(n + 1/2) * sqrt(1 + LambertW(exp(2/3)*(2*n - 1)/6)) * LambertW(exp(2/3)*(2*n - 1)/6)^n). - _Vaclav Kotesovec_, Oct 30 2022
%t A345747 Join[{1}, Table[n!*Sum[k^(n - 2*k)/k!, {k, 0, n/2}], {n, 1, 20}]] (* _Vaclav Kotesovec_, Oct 30 2022 *)
%o A345747 (PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)/k!);
%o A345747 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^(2*k)/(k!*(1-k*x)))))
%Y A345747 Cf. A354436, A355575.
%Y A345747 Cf. A104872, A216507, A356628.
%K A345747 nonn
%O A345747 0,3
%A A345747 _Seiichi Manyama_, Sep 17 2022