A205487 L.g.f.: Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - d*x^(n/d))^d.

1, 3, 10, 43, 206, 1104, 6581, 43227, 307927, 2351288, 19124238, 165102052, 1507907818, 14512524085, 146581677005, 1548261405595, 17054944088112, 195518380169283, 2328512358930925, 28759349826041248, 367752208054445945, 4860792910118985370

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Formula

Forms the logarithmic derivative of A205486.

Example

 L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 206*x^5/5 + 1104*x^6/6 +...
By definition:
L(x) = x/(1-x) + (x^2/2)/((1-x^2)*(1-2*x)^2) + (x^3/3)/((1-x^3)*(1-3*x)^3) + (x^4/4)/((1-x^4)*(1-2*x^2)^2*(1-4*x)^4) + (x^5/5)/((1-x^5)*(1-5*x)^5) + (x^6/6)/((1-x^6)*(1-2*x^3)^2*(1-3*x^2)^3*(1-6*x)^6) +...
Exponentiation yields the g.f. of A205486:
exp(L(x)) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 60*x^5 + 259*x^6 + 1273*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/d)+x*O(x^n))))), n)}

Crossrefs

Cf. A205486 (exp), A205477, A205479, A205481, A205483, A205485, A205489, A205491.

Sequence in context: A151085 A082936 A347006 * A323667 A030935 A132428

Adjacent sequences: A205484 A205485 A205486 * A205488 A205489 A205490

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved