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 A351891 #13 Feb 21 2025 05:57:33
%S A351891 1,1,1,3,9,25,105,443,1969,10609,57265,338547,2190969,14498185,
%T A351891 104277849,784965803,6150938593,51229928929,440694547681,
%U A351891 3967606065891,37247506348905,361022009762809,3645855348771273,38001754007842715,409302848055407761,4558828622414199121
%N A351891 Expansion of e.g.f. exp( sinh(sqrt(2)*x) / sqrt(2) ).
%F A351891 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * 2^k * a(n-2*k-1).
%F A351891 a(n) = Sum_{k=0..n} 2^((n-k)/2) * A136630(n,k). - _Seiichi Manyama_, Feb 20 2025
%t A351891 nmax = 25; CoefficientList[Series[Exp[Sinh[Sqrt[2] x]/Sqrt[2]], {x, 0, nmax}], x] Range[0, nmax]!
%t A351891 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 2 k] 2^k a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 25}]
%Y A351891 Cf. A003724, A009229, A055882, A136630, A351892, A381277.
%K A351891 nonn
%O A351891 0,4
%A A351891 _Ilya Gutkovskiy_, Feb 24 2022