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 A358065 #17 Nov 01 2022 12:16:34 %S A358065 1,1,2,6,48,360,2880,27720,322560,4173120,58665600,911433600, %T A358065 15567552000,287740252800,5710178073600,121450256928000, %U A358065 2758495490150400,66563938106265600,1699990278213427200,45828946821385728000,1300703752243703808000 %N A358065 Expansion of e.g.f. 1/(1 - x * exp(x^3)). %H A358065 Seiichi Manyama, <a href="/A358065/b358065.txt">Table of n, a(n) for n = 0..425</a> %F A358065 a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/k!. %F A358065 a(n) ~ n! * 3^(n/3) / ((1 + LambertW(3)) * LambertW(3)^(n/3)). - _Vaclav Kotesovec_, Nov 01 2022 %o A358065 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^3)))) %o A358065 (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k/k!); %Y A358065 Cf. A354553, A358064. %K A358065 nonn,easy %O A358065 0,3 %A A358065 _Seiichi Manyama_, Oct 29 2022