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 A356029 #46 Aug 19 2022 09:19:17
%S A356029 1,1,1,4,13,61,421,2626,27049,245953,3069721,40222216,576988501,
%T A356029 10058716669,169773404893,3596206855606,73450508303761,
%U A356029 1775382487932001,43993288886533489,1183551336464017708,34806599282992709341,1043452963148195577181
%N A356029 a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * (n - 2*k)!).
%F A356029 E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^2/2)).
%t A356029 a[n_] := n! * Sum[(n - 2*k)^k/(2^k*(n - 2*k)!), {k, 0, Floor[n/2]}]; a[0] = 1; Array[a, 22, 0] (* _Amiram Eldar_, Aug 19 2022 *)
%o A356029 (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*(n-2*k)!));
%o A356029 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^2/2)))))
%Y A356029 Cf. A354436, A356328, A356608.
%Y A356029 Cf. A354550, A356628, A356632.
%K A356029 nonn
%O A356029 0,4
%A A356029 _Seiichi Manyama_, Aug 18 2022