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 A380260 #16 Apr 29 2025 13:05:43
%S A380260 1,1,2,3,9,6,111,-573,7638,-95751,1450431,-24643134,468589617,
%T A380260 -9843336567,226448287794,-5662061186949,152892006728841,
%U A380260 -4434211761771978,137468475061977663,-4536657554920874181,158788359466681092966,-5875324355407515077439,229142457698060305226367
%N A380260 Expansion of e.g.f. exp( ((1+2*x)^(3/2) - 1)/3 ).
%H A380260 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F A380260 a(n) = Sum_{k=0..n} 2^(n-k) * Stirling1(n,k) * A004212(k) = Sum_{k=0..n} 3^k * 2^(n-k) * Stirling1(n,k) * Bell_k(1/3), where Bell_n(x) is n-th Bell polynomial.
%F A380260 a(n) = (1/exp(1/3)) * 2^n * n! * Sum_{k>=0} binomial(3*k/2,n)/(3^k * k!).
%t A380260 With[{nn=30},CoefficientList[Series[Exp[((1+2x)^(3/2)-1)/3],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 29 2025 *)
%o A380260 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(((1+2*x)^(3/2)-1)/3)))
%Y A380260 Cf. A049425, A380259.
%K A380260 sign
%O A380260 0,3
%A A380260 _Seiichi Manyama_, Jan 18 2025