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

1, 2, 6, 38, 490, 14152, 969444, 140621476, 46041241698, 36363843928316, 62022250535177416, 236043875222171125276, 2205302277098968939256248, 45728754995013679582534494332, 2070631745797418828103776968679204

Offset: 0

Author

Paul D. Hanna, Jan 20 2011

Keywords

• nonn

Examples

			The terms begin:
a(0) = 1;
a(1) = 1 + 1^2 = 2;
a(2) = 1 + 2^2 + 1^3 = 6;
a(3) = 1 + 3^2 + 3^3 + 1^4 = 38;
a(4) = 1 + 4^2 + 6^3 + 4^4 + 1^5 = 490;
a(5) = 1 + 5^2 + 10^3 + 10^4 + 5^5 + 1^6 = 14152.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..74

Crossrefs

Cf. A184730, A167008, A220359.

Programs

Mathematica

Table[Sum[Binomial[n, k]^(k+1), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 29 2014 *)

PARI

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

Formula

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

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