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

0,3

Comments

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

Links

Table of n, a(n) for n=0..17.

Example

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.

Prog

(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), ", "))

Crossrefs

Cf. A159604.

Sequence in context: A239981 A243549 A344418 * A009300 A192372 A304670

Adjacent sequences: A159592 A159593 A159594 * A159596 A159597 A159598

Keyword

nonn

Author

Paul D. Hanna, May 05 2009

Status

approved