A158107 - OEIS

%I #5 Mar 30 2012 18:37:16

%S 1,1,2,7,44,272,3053,25670,368728,4867442,86339238,1071067999,

%T 28751805809,417861397848,9791134239124,235308903842756,

%U 7238087265282704,133575559401222741,5068916834663575735

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

%F  G.f.: A(x) = Product_{n>=1} G_{n}(x^n) where G_{n}(x^n) = Product_{k=0..n-1} [1 + u^k*x * A(u^k*x)] with u = exp(2*Pi*I/n).

%e G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 44*x^4 + 272*x^5 + 3053*x^6 +...

%e log(1+x*A(x)) = x + x^2/2 + 4*x^3/3 + 21*x^4/4 + 186*x^5/5 + 1366*x^6/6 +...

%e log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 147*x^4/4 + 1116*x^5/5 + 16392*x^6/6 +...

%e log(A(x)) = x + 3*1*x^2/2 + 4*4*x^3/3 + 7*21*x^4/4 + 6*186*x^5/5 + 12*1366*x^6/6 +...

%o (PARI) {a(n)=local(A=1+x);if(n==0,1,for(i=1,n,A=exp(sum(m=1,n,sigma(m)*x^m*polcoeff(log(1+x*A+x*O(x^m)),m))+x*O(x^n)));polcoeff(A,n))}

%Y Cf. A158108.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 28 2009