A159308 - OEIS

%I #2 Mar 30 2012 18:37:17

%S 1,1,2,5,14,40,154,631,2246,10476,71232,383220,1553841,8223567,

%T 58756725,338290401,1754330940,11744499990,103864469131,1220564280222,

%U 17394859369497,214311637862464,1891506713163679,10894997683415647

%N G.f.: A(x) = exp( Sum_{n>=1} (1 + sigma(n)*x)^n * x^n/n ).

%e G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 40*x^5 + 154*x^6 +...

%e log(A(x)) = (1+x)*x + (1+3*x)^2*x^2/2 + (1+4*x)^3*x^3/3 + (1+7*x)^4*x^4/4 +...

%e log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 35*x^4/4 + 116*x^5/5 + 606*x^6/6 +... (A159309)

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

%Y Cf. A159309 (log).

%K nonn

%O 0,3

%A _Paul D. Hanna_, Apr 10 2009