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A184731 a(n) = Sum_{k=0..n} C(n,k)^(k+1). 8

%I

%S 1,2,6,38,490,14152,969444,140621476,46041241698,36363843928316,

%T 62022250535177416,236043875222171125276,2205302277098968939256248,

%U 45728754995013679582534494332,2070631745797418828103776968679204

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

%H Seiichi Manyama, <a href="/A184731/b184731.txt">Table of n, a(n) for n = 0..74</a>

%F Forms the logarithmic derivative of A184730 (ignoring the initial term).

%F 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 The terms begin:

%e a(0) = 1;

%e a(1) = 1 + 1^2 = 2;

%e a(2) = 1 + 2^2 + 1^3 = 6;

%e a(3) = 1 + 3^2 + 3^3 + 1^4 = 38;

%e a(4) = 1 + 4^2 + 6^3 + 4^4 + 1^5 = 490;

%e a(5) = 1 + 5^2 + 10^3 + 10^4 + 5^5 + 1^6 = 14152.

%t Table[Sum[Binomial[n, k]^(k+1), {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jan 29 2014 *)

%o (PARI) {a(n)=sum(k=0, n, binomial(n, k)^(k+1))}

%Y Cf. A184730, A167008, A220359.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 20 2011

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)