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 A380215 #15 Jan 19 2025 06:48:26
%S A380215 1,2,2,4,-12,152,-2056,34064,-663792,14890656,-378083936,10721383488,
%T A380215 -335898007232,11523599785856,-429685396446848,17303743585216768,
%U A380215 -748494039183318784,34612915914568045056,-1704065501541830102528,88989595986614229074944,-4913365756826406035999744
%N A380215 Expansion of e.g.f. exp( (1+3*x)^(2/3) - 1 ).
%F A380215 a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * Stirling1(n,k) * Bell(k).
%F A380215 a(n) = (1/e) * 3^n * n! * Sum_{k>=0} binomial(2*k/3,n)/k!.
%F A380215 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380261.
%F A380215 a(n) ~ (-1)^(n+1) * 2^(3/2) * sqrt(Pi) * 3^(n-1) * n^(n - 7/6) / (Gamma(1/3) * exp(n+1)). - _Vaclav Kotesovec_, Jan 19 2025
%o A380215 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((1+3*x)^(2/3)-1)))
%Y A380215 Cf. A380208, A380261.
%K A380215 sign
%O A380215 0,2
%A A380215 _Seiichi Manyama_, Jan 16 2025