A159595 G.f.: A(x) = exp( Sum_{n>=1} [ Sum_{k>=1} sigma(k,n)*x^k ]^n/n ).

1, 1, 4, 13, 56, 286, 2008, 19749, 280842, 5762129, 168873970, 7023348917, 412682000624, 34188301513404, 3992802803844526, 656649238572375132, 152278229304524217542, 49749953321847000835094

Offset: 0

Author

Paul D. Hanna, May 05 2009

Keywords

• nonn

Comments

Define sigma(k,n) = Sum_{d|k} d^n.

Examples

			G.f.: A(x) = 1 + x + 4*x^2 + 13*x^3 + 56*x^4 + 286*x^5 + 2008*x^6 +...
log(A(x)) = Sum_{n>=1} [x + sigma(2,n)*x^2 + sigma(3,n)*x^3 +...]^n/n.
		

Crossrefs

Cf. A159604.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,sum(k=1,n,sigma(k,m)*x^k+x*O(x^n))^m/m)));polcoeff(A,n)}
for(n=0,20,print1(a(n),", "))