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 A380309 #18 Jan 21 2025 05:00:00
%S A380309 1,-1,-3,-17,-143,-1601,-22419,-377217,-7415743,-166854657,
%T A380309 -4229195779,-119251176881,-3702809175823,-125546570425537,
%U A380309 -4615357640315603,-182855338776726561,-7766868454872857599,-352082642456714366977,-16965451818345573907843
%N A380309 Expansion of e.g.f. exp( 1 - 1/(1-3*x)^(1/3) ).
%H A380309 Seiichi Manyama, <a href="/A380309/b380309.txt">Table of n, a(n) for n = 0..382</a>
%F A380309 a(n) = Sum_{k=0..n} 3^(n-k) * |Stirling1(n,k)| * A000587(k).
%F A380309 a(n) = e * (-3)^n * n! * Sum_{k>=0} (-1)^k * binomial(-k/3,n)/k!.
%F A380309 a(0) = 1; a(n) = -Sum_{k=1..n} A007559(k) * binomial(n-1,k-1) * a(n-k).
%o A380309 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(1-1/(1-3*x)^(1/3))))
%Y A380309 Cf. A145561, A380308, A380310.
%Y A380309 Cf. A000587, A007559, A015735.
%K A380309 sign
%O A380309 0,3
%A A380309 _Seiichi Manyama_, Jan 20 2025