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G.f.: A(x) = exp( Sum_{n>=1} A179307(n)*x^n/n ), where A179307(n) = Sum_{d|n} C(n,d)*sigma(d)*sigma(n/d).
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%I #2 Mar 30 2012 18:37:22

%S 1,1,5,10,40,67,262,449,1572,2915,8876,16452,51811,93789,271500,

%T 518378,1457658,2734005,7584475,14282412,38649578,73773173,193491639,

%U 369696321,971226618,1845956358,4730626121,9114534520,23083308650,44287157822

%N G.f.: A(x) = exp( Sum_{n>=1} A179307(n)*x^n/n ), where A179307(n) = Sum_{d|n} C(n,d)*sigma(d)*sigma(n/d).

%e G.f.: A(x) = 1 + x + 5*x^2 + 10*x^3 + 40*x^4 + 67*x^5 + 262*x^6 +...

%e log(A(x)) = x + 9*x^2/2 + 16*x^3/3 + 89*x^4/4 + 36*x^5/5 + 504*x^6/6 +...

%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n,sumdiv(m,d,binomial(m,d)*sigma(d)*sigma(m/d))*x^m/m)+x*O(x^n)),n)}

%Y Cf. A179307.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 10 2010