%I #8 Jan 13 2025 16:26:47
%S 1,1,3,21,155,2691,18924,732230,9223166,269544904,4308339664,
%T 264486350330,3252603264996,283488024709418,5058264756924275,
%U 239269507574263597,9478611818612363119,788664781674375008343,13928483471031628860556,1889997256419148641470346
%N exp( Sum_{n>=1} A226561(n)*x^n/n ), where A226561(n) = Sum_{d|n} d^n*phi(d).
%e G.f.: A(x) = 1 + x + 3*x^2 + 21*x^3 + 155*x^4 + 2691*x^5 + 18924*x^6 +...
%e where
%e log(A(x)) = x + 5*x^2/2 + 55*x^3/3 + 529*x^4/4 + 12501*x^5/5 + 94835*x^6/6 + 4941259*x^7/7 + 67240193*x^8/8 +...+ A226561(n)*x^n/n +...
%o (PARI) {A226561(n)=sumdiv(n, d, d*eulerphi(d^n))}
%o {a(n)=polcoeff(exp(sum(k=1,n,A226561(k)*x^k/k)+x*O(x^n)),n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A226561, A226458.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 10 2013