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 A370669 #10 Feb 25 2024 09:08:53
%S A370669 1,1,2,5,20,103,630,4475,36232,329341,3320890,36787889,444125628,
%T A370669 5803850515,81625106990,1229298774647,19738870726160,336627732586105,
%U A370669 6076590994501938,115752541255203869,2320456607696181220,48833227436258924671,1076420625931284514342
%N A370669 Expansion of Sum_{k>=0} k! * ( x/(1+x^2) )^k.
%F A370669 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-2*k)! * binomial(n-k-1,k).
%F A370669 a(n) = n*a(n-1) + (n-4)*a(n-3) + a(n-4) for n > 4.
%o A370669 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x/(1+x^2))^k))
%o A370669 (PARI) a(n) = sum(k=0, n\2, (-1)^k*(n-2*k)!*binomial(n-k-1, k));
%Y A370669 Cf. A000255, A370670.
%Y A370669 Cf. A177249, A212580, A276080.
%K A370669 nonn
%O A370669 0,3
%A A370669 _Seiichi Manyama_, Feb 25 2024