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 A358265 #14 Mar 13 2023 16:04:03
%S A358265 1,1,2,6,28,160,1080,8470,76160,771120,8671600,107245600,1446984000,
%T A358265 21150929800,332950217600,5615507898000,101024594070400,
%U A358265 1931055071545600,39082823446867200,834945681049480000,18776164188349568000,443348081412556320000
%N A358265 Expansion of e.g.f. 1/(1 - x * exp(x^3/6)).
%F A358265 a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(6^k * k!).
%F A358265 a(n) ~ n! / ((1 + LambertW(1/2)) * (2*LambertW(1/2))^(n/3)). - _Vaclav Kotesovec_, Nov 13 2022
%p A358265 g := 1/(1-x*exp(x^3/6)) ;
%p A358265 taylor(%,x=0,70) ;
%p A358265 L := gfun[seriestolist](%) ;
%p A358265 seq( op(i,L)*(i-1)!,i=1..nops(L)) ; # _R. J. Mathar_, Mar 13 2023
%o A358265 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^3/6))))
%o A358265 (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(6^k*k!));
%Y A358265 Cf. A006153, A358264.
%Y A358265 Cf. A354551, A358065.
%K A358265 nonn,easy
%O A358265 0,3
%A A358265 _Seiichi Manyama_, Nov 06 2022