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%I #10 Jul 07 2022 02:44:15
%S 1,3,7,39,366,5697,194881,16288695,2430565261,564615230758,
%T 257227244037248,319346787227133873,832952161388710135215,
%U 3382434539389226013260403,22966972221673234523620345857
%N a(n) = Sum_{k=0..[n/2]} C(n-k,k)^(n-k)*n/(n-k), n>=1.
%H G. C. Greubel, <a href="/A166895/b166895.txt">Table of n, a(n) for n = 1..50</a>
%F Logarithmic derivative of A166894.
%e 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 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 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 (PARI) a(n)=sum(k=0,n\2,binomial(n-k,k)^(n-k)*n/(n-k))
%Y Cf. A166894, A209428.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Nov 23 2009
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