A159604 G.f.: A(x) = exp( Sum_{n>=1} [ Sum_{k>=1} sigma(n,k)*x^k ]^n/n ).

1, 1, 6, 43, 856, 10744, 608375, 14284223, 551011548, 19119025101, 874788949035, 37896009869060, 20683158266928833, 1799893777863733707, 93147805938921355288, 3757831283217050847983, 180287028377782585130749

Offset: 0

Author

Paul D. Hanna, May 16 2009

Keywords

• nonn

Comments

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

Examples

			G.f.: A(x) = 1 + x + 6*x^2 + 43*x^3 + 856*x^4 + 10744*x^5 +...
log(A(x)) = Sum_{n>=1} [sigma(n)*x + sigma(n,2)*x^2 + sigma(n,3)*x^3 +...]^n/n.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..510

Crossrefs

Cf. variants: A159595, A156217.

Programs

PARI

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