A205491 L.g.f.: Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - d*x^d)^n.

1, 3, 7, 23, 51, 165, 386, 1039, 2554, 6963, 17260, 47825, 124840, 340658, 911037, 2484687, 6614616, 17735646, 46647167, 122536323, 318125129, 825153684, 2130076369, 5522611009, 14375957026, 37817347272, 100579846732, 271246531726, 740731197176

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Formula

Forms the logarithmic derivative of A205490.

Example

 L.g.f.: L(x) = x + 3*x^2/2 + 7*x^3/3 + 23*x^4/4 + 51*x^5/5 + 165*x^6/6 +...
By definition:
L(x) = x/(1-x) + (x^2/2)/((1-x)^2*(1-2*x^2)^2) + (x^3/3)/((1-x)^3*(1-3*x^3)^3) + (x^4/4)/((1-x)^4*(1-2*x^2)^4*(1-4*x^4)^4) + (x^5/5)/((1-x)^5*(1-5*x^5)^5) + (x^6/6)/((1-x)^6*(1-2*x^2)^6*(1-3*x^3)^6*(1-6*x^6)^6) +...
Exponentiation yields the g.f. of A205490:
exp(L(x)) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 22*x^5 + 57*x^6 + 134*x^7 +...

Prog

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

Crossrefs

Cf. A205490 (exp), A205477, A205479, A205481, A205483, A205485, A205487, A205489.

Sequence in context: A246497 A002715 A112052 * A203253 A179491 A219167

Adjacent sequences: A205488 A205489 A205490 * A205492 A205493 A205494

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved