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a(n) = Sum_{d|n} C(n,d)^(n/d).
3

%I #9 Oct 08 2021 22:35:18

%S 1,5,28,293,3126,50432,823544,17396773,388013194,10184591630,

%T 285311670612,9001219099424,302875106592254,11163682939272372,

%U 437913418466474778,18489753215468948517,827240261886336764178

%N a(n) = Sum_{d|n} C(n,d)^(n/d).

%H Seiichi Manyama, <a href="/A174464/b174464.txt">Table of n, a(n) for n = 1..386</a>

%F Logarithmic derivative of A174463.

%F a(n) ~ n^n. - _Vaclav Kotesovec_, Oct 05 2020

%t Table[Sum[Binomial[n,d]^(n/d), {d,Divisors[n]}], {n,1,20}] (* _Vaclav Kotesovec_, Oct 05 2020 *)

%o (PARI) {a(n)=sumdiv(n,d,binomial(n,d)^(n/d))}

%Y Cf. A174463.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Apr 04 2010