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A159604 G.f.: A(x) = exp( Sum_{n>=1} [ Sum_{k>=1} sigma(n,k)*x^k ]^n/n ). 0
1, 1, 6, 43, 856, 10744, 608375, 14284223, 551011548, 19119025101, 874788949035, 37896009869060, 20683158266928833, 1799893777863733707, 93147805938921355288, 3757831283217050847983, 180287028377782585130749 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..16.

EXAMPLE

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.

PROG

(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)}

CROSSREFS

Cf. variants: A159595, A156217.

Sequence in context: A062266 A217485 A290783 * A090338 A090339 A225159

Adjacent sequences:  A159601 A159602 A159603 * A159605 A159606 A159607

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 16 2009

STATUS

approved

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Last modified July 4 14:29 EDT 2020. Contains 335448 sequences. (Running on oeis4.)