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 A375610 #15 Aug 21 2024 11:21:50
%S A375610 1,1,1,7,49,241,1681,18481,192193,2028097,26854561,400419361,
%T A375610 6074016961,100260498625,1847840462833,36061045391281,738757221740161,
%U A375610 16244778936351361,380460397886975809,9341152506044172865,241084169507148900481,6559259107807215358081
%N A375610 Expansion of e.g.f. 1 / (exp(-x) - x^3).
%F A375610 a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(n-3*k)/(n-3*k)!.
%F A375610 a(n) == 1 (mod 6).
%F A375610 a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / ((1 + LambertW(1/3)) * 3^(n+4) * exp(n) * LambertW(1/3)^(n+3)). - _Vaclav Kotesovec_, Aug 21 2024
%o A375610 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x)-x^3)))
%o A375610 (PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(n-3*k)/(n-3*k)!);
%Y A375610 Cf. A072597, A352303.
%K A375610 nonn
%O A375610 0,4
%A A375610 _Seiichi Manyama_, Aug 21 2024