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 A323768 #23 Feb 28 2024 10:50:17
%S A323768 1,1,2,3,5,14,43,171,1234,9075,94295,1685324,28688843,804627839,
%T A323768 34189166176,1379425012899,106952499421507,10394354507270548,
%U A323768 1052079100669253203,221582922117645427461,48152920476428200426258,13152336142340905111739041
%N A323768 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)^k.
%H A323768 Seiichi Manyama, <a href="/A323768/b323768.txt">Table of n, a(n) for n = 0..123</a>
%F A323768 Limit_{n->infinity} a(n)^(1/n^2) = ((1-r)/r)^(r^2/(4*r-1)) = 1.17123387669321050316385592324128471190583619526359450226558587879190245..., where r = A323773 = 0.3663201503052830964087236563781171194011826607210994595... is the root of the equation (1-2*r)^(4*r-1) * (1-r)^(1-2*r) = r^(2*r).
%t A323768 Table[Sum[Binomial[n-k, k]^k, {k, 0, n/2}], {n, 0, 25}]
%o A323768 (PARI) {a(n) = sum(k=0, n\2, binomial(n-k, k)^k)} \\ _Seiichi Manyama_, Jan 27 2019
%Y A323768 Cf. A323769, A295612.
%K A323768 nonn
%O A323768 0,3
%A A323768 _Vaclav Kotesovec_, Jan 27 2019