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 A380258 #15 Mar 31 2025 22:02:07
%S A380258 1,1,8,106,1954,46082,1323064,44750644,1741897340,76672512316,
%T A380258 3764746706176,203976645319448,12086590557877144,777464693554778776,
%U A380258 53948773488864143072,4016672567726156437744,319379204127841984947472,27010128651142535536409360,2420802590890201251989984128
%N A380258 Expansion of e.g.f. exp( (1/(1-5*x)^(2/5) - 1)/2 ).
%H A380258 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F A380258 a(n) = Sum_{k=0..n} 5^(n-k) * |Stirling1(n,k)| * A004211(k) = Sum_{k=0..n} 2^k * 5^(n-k) * |Stirling1(n,k)| * Bell_k(1/2), where Bell_n(x) is n-th Bell polynomial.
%F A380258 a(n) = (1/exp(1/2)) * (-5)^n * n! * Sum_{k>=0} binomial(-2*k/5,n)/(2^k * k!).
%t A380258 CoefficientList[Series[Exp[ (1/(1-5*x)^(2/5) - 1)/2 ],{x,0,18}],x]Range[0,18]! (* _Stefano Spezia_, Mar 31 2025 *)
%o A380258 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1/(1-5*x)^(2/5)-1)/2)))
%Y A380258 Cf. A049376, A375173, A380257.
%Y A380258 Cf. A004211, A025168.
%K A380258 nonn
%O A380258 0,3
%A A380258 _Seiichi Manyama_, Jan 18 2025