A205489 L.g.f.: Sum_{n>=1} (x^n/n) / Product_{d|n} (1 - d*x^n)^d.

1, 3, 4, 15, 6, 78, 8, 247, 202, 708, 12, 4146, 14, 5498, 8964, 24135, 18, 81114, 20, 206520, 193736, 225558, 24, 2314378, 242656, 1278332, 3622954, 9209950, 30, 26654118, 32, 58890983, 59213598, 35652216, 28736938, 628796418, 38, 179307278, 878319368

Offset

1,2

Links

Table of n, a(n) for n=1..39.

Formula

Forms the logarithmic derivative of A205488.

Example

 L.g.f.: L(x) = x + 3*x^2/2 + 4*x^3/3 + 15*x^4/4 + 6*x^5/5 + 78*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^4)^2*(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^6)^2*(1-3*x^6)^3*(1-6*x^6)^6) +...
Exponentiation yields the g.f. of A205488:
exp(L(x)) = 1 + x + 2*x^2 + 3*x^3 + 7*x^4 + 9*x^5 + 26*x^6 + 32*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. A205488 (exp), A205477, A205479, A205481, A205483, A205485, A205487, A205491.

Sequence in context: A157351 A071167 A194924 * A343935 A280685 A076365

Adjacent sequences: A205486 A205487 A205488 * A205490 A205491 A205492

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved