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A184731 a(n) = Sum_{k=0..n} C(n,k)^(k+1).

%I A184731 #10 Jan 10 2019 11:17:34
%S A184731 1,2,6,38,490,14152,969444,140621476,46041241698,36363843928316,
%T A184731 62022250535177416,236043875222171125276,2205302277098968939256248,
%U A184731 45728754995013679582534494332,2070631745797418828103776968679204
%N A184731 a(n) = Sum_{k=0..n} C(n,k)^(k+1).
%H A184731 Seiichi Manyama, <a href="/A184731/b184731.txt">Table of n, a(n) for n = 0..74</a>
%F A184731 Forms the logarithmic derivative of A184730 (ignoring the initial term).
%F A184731 Limit n->infinity a(n)^(1/n^2) = (1-r)^(-r/2) = 1.53362806511..., where r = 0.70350607643... (see A220359) is the root of the equation (1-r)^(2*r-1) = r^(2*r). - _Vaclav Kotesovec_, Jan 29 2014
%e A184731 The terms begin:
%e A184731 a(0) = 1;
%e A184731 a(1) = 1 + 1^2 = 2;
%e A184731 a(2) = 1 + 2^2 + 1^3 = 6;
%e A184731 a(3) = 1 + 3^2 + 3^3 + 1^4 = 38;
%e A184731 a(4) = 1 + 4^2 + 6^3 + 4^4 + 1^5 = 490;
%e A184731 a(5) = 1 + 5^2 + 10^3 + 10^4 + 5^5 + 1^6 = 14152.
%t A184731 Table[Sum[Binomial[n, k]^(k+1), {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jan 29 2014 *)
%o A184731 (PARI) {a(n)=sum(k=0, n, binomial(n, k)^(k+1))}
%Y A184731 Cf. A184730, A167008, A220359.
%K A184731 nonn
%O A184731 0,2
%A A184731 _Paul D. Hanna_, Jan 20 2011