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 A380257 #17 Mar 31 2025 22:01:59
%S A380257 1,1,6,56,706,11186,213156,4742256,120571676,3447128796,109427729096,
%T A380257 3818008773536,145196289453656,5976489668054296,264685744187399536,
%U A380257 12548508890339297856,634022724191046592016,34007862777419093053456,1929842567333195106456416
%N A380257 Expansion of e.g.f. exp( (1/(1-3*x)^(2/3) - 1)/2 ).
%H A380257 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F A380257 a(n) = Sum_{k=0..n} 3^(n-k) * |Stirling1(n,k)| * A004211(k) = Sum_{k=0..n} 2^k * 3^(n-k) * |Stirling1(n,k)| * Bell_k(1/2), where Bell_n(x) is n-th Bell polynomial.
%F A380257 a(n) = (1/exp(1/2)) * (-3)^n * n! * Sum_{k>=0} binomial(-2*k/3,n)/(2^k * k!).
%t A380257 CoefficientList[Series[Exp[ (1/(1-3*x)^(2/3) - 1)/2 ],{x,0,18}],x]Range[0,18]! (* _Stefano Spezia_, Mar 31 2025 *)
%o A380257 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1/(1-3*x)^(2/3)-1)/2)))
%Y A380257 Cf. A049376, A375173, A380258.
%Y A380257 Cf. A004211, A380214.
%K A380257 nonn
%O A380257 0,3
%A A380257 _Seiichi Manyama_, Jan 18 2025