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 A370509 #14 Feb 20 2024 13:46:46
%S A370509 1,1,2,7,28,138,818,5658,44784,399366,3962256,43289760,516432984,
%T A370509 6679346280,93091875120,1390851720840,22175338353120,375794883339120,
%U A370509 6745177713093840,127830886641354960,2550687440585679360,53451172032327664560,1173650135526055272960
%N A370509 Expansion of Sum_{k>=0} k! * ( x * (1+x^2) )^k.
%F A370509 a(n) = Sum_{k=0..floor(n/3)} (n-2*k)! * binomial(n-2*k,k).
%o A370509 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1+x^2))^k))
%o A370509 (PARI) a(n) = sum(k=0, n\3, (n-2*k)!*binomial(n-2*k, k));
%Y A370509 Cf. A240172, A370510.
%Y A370509 Cf. A212580.
%K A370509 nonn,easy
%O A370509 0,3
%A A370509 _Seiichi Manyama_, Feb 20 2024