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 A380208 #22 Jan 21 2025 04:59:54
%S A380208 1,1,-1,5,-39,421,-5809,97609,-1933455,44107881,-1138752449,
%T A380208 32820576141,-1044523471991,36379398867085,-1376300966184689,
%U A380208 56200996031812241,-2463713702730471199,115400572452587463249,-5751849729149085927425,303954806150664749166101
%N A380208 Expansion of e.g.f. exp( (1+3*x)^(1/3) - 1 ).
%H A380208 Seiichi Manyama, <a href="/A380208/b380208.txt">Table of n, a(n) for n = 0..381</a>
%F A380208 a(n) = Sum_{k=0..n} 3^(n-k) * Stirling1(n,k) * Bell(k).
%F A380208 a(n) = (1/e) * 3^n * n! * Sum_{k>=0} binomial(k/3,n)/k!.
%F A380208 a(0) = 1; a(n) = Sum_{k=1..n} (Product_{j=0..k-1} (-3*j+1)) * binomial(n-1,k-1) * a(n-k).
%o A380208 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1+3*x)^(1/3)-1)))
%Y A380208 Cf. A000806, A380307.
%Y A380208 Cf. A373713, A380215, A380229.
%K A380208 sign
%O A380208 0,4
%A A380208 _Seiichi Manyama_, Jan 16 2025