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 A357598 #27 Feb 16 2025 08:34:04
%S A357598 0,1,1,5,25,117,601,3509,22457,153141,1105561,8453557,68339833,
%T A357598 581495605,5184047961,48259748533,468040609593,4719817792565,
%U A357598 49396003390489,535526127566773,6004124908829177,69509047405180213,829801009239621849,10202835010223731893
%N A357598 Expansion of e.g.f. sinh(2 * (exp(x)-1)) / 2.
%H A357598 Seiichi Manyama, <a href="/A357598/b357598.txt">Table of n, a(n) for n = 0..558</a>
%H A357598 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F A357598 a(n) = Sum_{k=0..floor((n-1)/2)} 4^k * Stirling2(n,2*k+1).
%F A357598 a(n) = ( Bell_n(2) - Bell_n(-2) )/4, where Bell_n(x) is n-th Bell polynomial.
%F A357598 a(n) = 0; a(n) = Sum_{k=0..n-1} binomial(n-1, k) * A065143(k).
%o A357598 (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh(2*(exp(x)-1))/2)))
%o A357598 (PARI) a(n) = sum(k=0, (n-1)\2, 4^k*stirling(n, 2*k+1, 2));
%o A357598 (PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
%o A357598 a(n) = round((Bell_poly(n, 2)-Bell_poly(n, -2)))/4;
%Y A357598 Cf. A024429, A264037, A357572.
%Y A357598 Cf. A065143, A078944, A357599.
%K A357598 nonn
%O A357598 0,4
%A A357598 _Seiichi Manyama_, Oct 05 2022