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 A166895 #14 Nov 20 2024 08:08:31
%S A166895 1,3,7,39,366,5697,194881,16288695,2430565261,564615230758,
%T A166895 257227244037248,319346787227133873,832952161388710135215,
%U A166895 3382434539389226013260403,22966972221673234523620345857
%N A166895 a(n) = Sum_{k=0..[n/2]} C(n-k,k)^(n-k)*n/(n-k), n>=1.
%H A166895 G. C. Greubel, <a href="/A166895/b166895.txt">Table of n, a(n) for n = 1..50</a>
%F A166895 Logarithmic derivative of A166894.
%F A166895 Limit_{n->oo} a(n)^(1/n^2) = (1/r - 1)^((1 - r)^2/(3 - 4*r)) = 1.436094496902535711953511352318447104797138641971237143543..., where r = A323777 = 0.220676041323740696312822269998050167187681031027574... is the root of the equation (1 - 2*r)^(3 - 4*r) = (1 - r)^(2*(1 - r))*r^(1 - 2*r). - _Vaclav Kotesovec_, Nov 20 2024
%e A166895 L.g.f.: L(x) = x + 3*x^2/2 + 7*x^3/3 + 39*x^4/4 + 366*x^5/5 + 5697*x^6/6 +...
%e A166895 exp(L(x)) = 1 + x + 2*x^2 + 4*x^3 + 14*x^4 + 89*x^5 + 1050*x^6 +...+ A166894(n)*x^n +...
%t A166895 Table[Sum[Binomial[n - k, k]^(n - k) *n/(n - k), {k, 0, Floor[n/2]}], {n, 1, 25}] (* _G. C. Greubel_, May 27 2016 *)
%o A166895 (PARI) a(n)=sum(k=0,n\2,binomial(n-k,k)^(n-k)*n/(n-k))
%Y A166895 Cf. A166894, A209428.
%K A166895 nonn
%O A166895 1,2
%A A166895 _Paul D. Hanna_, Nov 23 2009