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 A357727 #23 Feb 16 2025 08:34:04
%S A357727 1,0,-4,-12,-12,100,852,4004,9940,-36828,-726316,-6174300,-35968812,
%T A357727 -109708508,702818004,16677814436,188794428628,1542659688996,
%U A357727 8359981681364,-3068614764636,-868989327994668,-15076627082974940,-179727483880747308
%N A357727 Expansion of e.g.f. cos( 2 * (exp(x) - 1) ).
%H A357727 Andrew Howroyd, <a href="/A357727/b357727.txt">Table of n, a(n) for n = 0..200</a>
%H A357727 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%F A357727 a(n) = Sum_{k=0..floor(n/2)} (-4)^k * Stirling2(n,2*k).
%F A357727 a(n) = 1; a(n) = -4 * Sum_{k=0..n-1} binomial(n-1, k) * A357738(k).
%F A357727 a(n) = ( Bell_n(2 * i) + Bell_n(-2 * i) )/2, where Bell_n(x) is n-th Bell polynomial and i is the imaginary unit.
%o A357727 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(cos(2*(exp(x)-1))))
%o A357727 (PARI) a(n) = sum(k=0, n\2, (-4)^k*stirling(n, 2*k, 2));
%o A357727 (PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
%o A357727 a(n) = round((Bell_poly(n, 2*I)+Bell_poly(n, -2*I)))/2;
%Y A357727 Column k=4 of A357728.
%Y A357727 Cf. A065143, A357719, A357738.
%K A357727 sign
%O A357727 0,3
%A A357727 _Seiichi Manyama_, Oct 10 2022