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A184731
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a(n) = Sum_{k=0..n} C(n,k)^(k+1).
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8
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1, 2, 6, 38, 490, 14152, 969444, 140621476, 46041241698, 36363843928316, 62022250535177416, 236043875222171125276, 2205302277098968939256248, 45728754995013679582534494332, 2070631745797418828103776968679204
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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EXAMPLE
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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.
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MATHEMATICA
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Table[Sum[Binomial[n, k]^(k+1), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 29 2014 *)
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PROG
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(PARI) {a(n)=sum(k=0, n, binomial(n, k)^(k+1))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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