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 A380262 #12 Feb 16 2025 08:34:07
%S A380262 1,1,-2,16,-206,3682,-84236,2348704,-77241380,2926735516,
%T A380262 -125540336024,6013069027648,-318093606114536,18418565715581656,
%U A380262 -1158626159228481488,78679416565851286144,-5736477278907382585328,446936684375920051751440,-37056888825921886749507872
%N A380262 Expansion of e.g.f. exp( ((1+5*x)^(2/5) - 1)/2 ).
%H A380262 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F A380262 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 A380262 a(n) = (1/exp(1/2)) * 5^n * n! * Sum_{k>=0} binomial(2*k/5,n)/(2^k * k!).
%o A380262 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(((1+5*x)^(2/5)-1)/2)))
%Y A380262 Cf. A000085, A002119, A380261.
%K A380262 sign
%O A380262 0,3
%A A380262 _Seiichi Manyama_, Jan 18 2025