A205483 L.g.f.: Sum_{n>=1} x^n/n * Product_{d|n} (1 + d*x^n)^d.

1, 3, 1, 11, 1, 45, 1, 59, 109, 53, 1, 869, 1, 101, 961, 3643, 1, 3555, 1, 18101, 3235, 245, 1, 92645, 21876, 341, 11287, 74141, 1, 722045, 1, 324667, 20329, 581, 502076, 5280611, 1, 725, 40054, 7567509, 1, 27239663, 1, 906301, 7838224, 1061, 1, 181474021

Offset

1,2

Links

Table of n, a(n) for n=1..48.

Formula

Forms the logarithmic derivative of A205482.

Example

 L.g.f.: L(x) = x + 3*x^2/2 + x^3/3 + 11*x^4/4 + x^5/5 + 45*x^6/6 +...
By definition:
L(x) = x*(1+x) + x^2*(1+x^2)*(1+2*x^2)^2/2 + x^3*(1+x^3)*(1+3*x^3)^3/3 + x^4*(1+x^4)*(1+2*x^4)^2*(1+4*x^4)^4/4 + x^5*(1+x^5)*(1+5*x^5)^5/5 + x^6*(1+x^6)*(1+2*x^6)^2*(1+3*x^6)^3*(1+6*x^6)^6/6 +...
Exponentiation yields the g.f. of A205482:
exp(L(x)) = 1 + x + 2*x^2 + 2*x^3 + 5*x^4 + 5*x^5 + 15*x^6 + 15*x^7 +...

Prog

 (PARI) {a(n)=n*polcoeff(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, d*log(1+d*x^m+x*O(x^n))))), n)}

Crossrefs

Cf. A205482 (exp), A205477, A205479, A205481, A205485, A205487, A205489, A205491.

Sequence in context: A339175 A134761 A166752 * A230262 A323854 A256589

Adjacent sequences: A205480 A205481 A205482 * A205484 A205485 A205486

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved