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 A352279 #19 Feb 18 2025 08:56:40
%S A352279 1,2,4,10,32,114,448,1978,9472,48738,270336,1595114,9965568,65852882,
%T A352279 457326592,3329243546,25356271616,201326396098,1663597019136,
%U A352279 14279558011850,127044810702848,1170023757062450,11136610150121472,109395885009537402,1107781178494025728,11549900930966957346
%N A352279 a(0) = 1; a(n) = 2 * Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * a(n-2*k-1).
%H A352279 Seiichi Manyama, <a href="/A352279/b352279.txt">Table of n, a(n) for n = 0..576</a>
%F A352279 E.g.f.: exp( 2 * sinh(x) ).
%F A352279 a(n) = Sum_{k=0..n} 2^k * A136630(n,k). - _Seiichi Manyama_, Feb 18 2025
%t A352279 a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[n - 1, 2 k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 25}]
%t A352279 nmax = 25; CoefficientList[Series[Exp[2 Sinh[x]], {x, 0, nmax}], x] Range[0, nmax]!
%t A352279 Table[Sum[(-1)^k * Binomial[n, k] * BellB[k, -1] * BellB[n-k], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jun 27 2022 *)
%o A352279 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(2*sinh(x)))) \\ _Seiichi Manyama_, Mar 26 2022
%Y A352279 Cf. A000557, A000807, A001861.
%Y A352279 Cf. A003724, A136630, A352280.
%K A352279 nonn
%O A352279 0,2
%A A352279 _Ilya Gutkovskiy_, Mar 10 2022