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 A375632 #7 Aug 22 2024 09:17:04
%S A375632 1,2,4,9,28,122,624,3523,22824,170948,1422664,12856373,126598036,
%T A375632 1358773886,15721899652,194356158823,2560950546576,35899907132872,
%U A375632 533099244285136,8351271711094697,137675784924101596,2383758487476054242,43244905386257120044
%N A375632 Expansion of e.g.f. exp(2*x) / (1 - x^3/6 * exp(x)).
%F A375632 a(n) = n! * Sum_{k=0..floor(n/3)} (k+2)^(n-3*k)/(6^k*(n-3*k)!).
%o A375632 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^3/6*exp(x))))
%o A375632 (PARI) a(n) = n!*sum(k=0, n\3, (k+2)^(n-3*k)/(6^k*(n-3*k)!));
%Y A375632 Cf. A368265, A375631.
%K A375632 nonn
%O A375632 0,2
%A A375632 _Seiichi Manyama_, Aug 22 2024