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 A357668 #25 Feb 16 2025 08:34:04
%S A357668 0,1,1,10,55,307,2026,14779,114157,933616,8110261,74525167,719925328,
%T A357668 7279859485,76855303981,845280487018,9663800287483,114601481983855,
%U A357668 1407040763488354,17856103120048783,233883061849700137,3157648445216335528,43887908697233605489
%N A357668 Expansion of e.g.f. sinh( 3 * (exp(x) - 1) )/3.
%H A357668 Seiichi Manyama, <a href="/A357668/b357668.txt">Table of n, a(n) for n = 0..547</a>
%H A357668 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F A357668 a(n) = Sum_{k=0..floor((n-1)/2)} 9^k * Stirling2(n,2*k+1).
%F A357668 a(n) = ( Bell_n(3) - Bell_n(-3) )/6, where Bell_n(x) is n-th Bell polynomial.
%F A357668 a(n) = 0; a(n) = Sum_{k=0..n-1} binomial(n-1, k) * A357667(k).
%o A357668 (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh(3*(exp(x)-1))/3)))
%o A357668 (PARI) a(n) = sum(k=0, (n-1)\2, 9^k*stirling(n, 2*k+1, 2));
%o A357668 (PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
%o A357668 a(n) = round((Bell_poly(n, 3)-Bell_poly(n, -3)))/6;
%Y A357668 Cf. A024429, A264037, A357572, A357598.
%Y A357668 Cf. A027710, A356572, A357667.
%K A357668 nonn
%O A357668 0,4
%A A357668 _Seiichi Manyama_, Oct 08 2022