A158107 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)).

1, 1, 2, 7, 44, 272, 3053, 25670, 368728, 4867442, 86339238, 1071067999, 28751805809, 417861397848, 9791134239124, 235308903842756, 7238087265282704, 133575559401222741, 5068916834663575735

Offset: 0

Author

Paul D. Hanna, Mar 28 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 44*x^4 + 272*x^5 + 3053*x^6 +...
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 +...
log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 147*x^4/4 + 1116*x^5/5 + 16392*x^6/6 +...
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 +...
		

Crossrefs

Cf. A158108.

Programs

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))}

Formula

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).