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G.f.: A(x) = Sum_{n>=0} log(1 + Sum_{k>=1} k^n*x^k )^n/n!.
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%I #2 Mar 30 2012 18:37:17

%S 1,1,2,5,16,62,312,2001,16796,183416,2634814,49703026,1240433524,

%T 40975503423,1803618092422,105967390883387,8362303039735026,

%U 888404336012975536,127771790716640691664,24942884185805223709166

%N G.f.: A(x) = Sum_{n>=0} log(1 + Sum_{k>=1} k^n*x^k )^n/n!.

%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 62*x^5 +...

%e A(x) = Sum_{n>=0} log(1 + x + 2^n*x^2 + 3^n*x^3 + 4^n*x^4 +..)^n/n!

%o (PARI) {a(n)=polcoeff(sum(m=0,n,log(1+sum(k=1,n,k^m*x^k)+x*O(x^n))^m/m!),n)}

%Y Cf. A136553 (variant).

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 08 2009