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 A357580 #24 Oct 14 2022 16:28:48
%S A357580 1,1,2,5,16,57,232,1017,4864,24641,133024,752765,4476928,27707513,
%T A357580 178613376,1191756593,8231124992,58598528065,429868937728,
%U A357580 3239768599221,25073052286976,198825601967609,1614604933769216,13405327061690025,113725655719346176
%N A357580 a(n) = ((1 + sqrt(n))^n - (1 - sqrt(n))^n)/(2*n*sqrt(n)).
%H A357580 Alois P. Heinz, <a href="/A357580/b357580.txt">Table of n, a(n) for n = 1..698</a>
%F A357580 a(n) = A357502(n)/n.
%F A357580 From _Alois P. Heinz_, Oct 04 2022: (Start)
%F A357580 a(n) = [x^n] x/(n*(1-2*x-(n-1)*x^2)).
%F A357580 a(n) = Sum_{j=0..floor(n/2)} n^(j-1) * binomial(n,2*j+1).
%F A357580 a(n) = A099173(n,n)/n. (End)
%p A357580 b:= proc(n, k) option remember;
%p A357580 `if`(n<2, n, 2*b(n-1, k)+(k-1)*b(n-2, k))
%p A357580 end:
%p A357580 a:= n-> b(n$2)/n:
%p A357580 seq(a(n), n=1..25); # _Alois P. Heinz_, Oct 04 2022
%t A357580 Expand[Table[((1 + Sqrt[n])^n - (1 - Sqrt[n])^n)/(2*n*Sqrt[n]), {n, 1, 27}]]
%o A357580 (Python)
%o A357580 from sympy import simplify, sqrt
%o A357580 def A357580(n): return simplify(((1+sqrt(n))**n-(1-sqrt(n))**n)/(n*sqrt(n)))>>1 # _Chai Wah Wu_, Oct 14 2022
%Y A357580 Cf. A099173, A357502.
%K A357580 nonn
%O A357580 1,3
%A A357580 _Alexander R. Povolotsky_, Oct 04 2022