A205481 L.g.f.: Sum_{n>=1} x^n/n * Product_{d|n} (1 + d*x^(n/d))^d.

1, 3, 7, 23, 76, 249, 974, 4151, 16558, 70308, 342937, 1680725, 8012252, 40903572, 222539812, 1202060807, 6608077855, 38523427818, 228629565951, 1349303611408, 8257330774574, 53118486147015, 345693735519287, 2252515985849693, 15028013765653626, 102689873016938288

Offset

1,2

Links

Table of n, a(n) for n=1..26.

Formula

Forms the logarithmic derivative of A205480.

Example

 L.g.f.: L(x) = x + 3*x^2/2 + 7*x^3/3 + 23*x^4/4 + 76*x^5/5 + 249*x^6/6 +...
By definition:
L(x) = x*(1+x) + x^2*(1+x^2)*(1+2*x)^2/2 + x^3*(1+x^3)*(1+3*x)^3/3 + x^4*(1+x^4)*(1+2*x^2)^2*(1+4*x)^4/4 + x^5*(1+x^5)*(1+5*x)^5/5 + x^6*(1+x^6)*(1+2*x^3)^2*(1+3*x^2)^3*(1+6*x)^6/6 +...
Exponentiation yields the g.f. of A205480:
exp(L(x)) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 27*x^5 + 76*x^6 + 242*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. A205480 (exp), A205477, A205479, A205483, A205485, A205487, A205489, A205491.

Sequence in context: A148710 A148711 A344775 * A341071 A148712 A208591

Adjacent sequences: A205478 A205479 A205480 * A205482 A205483 A205484

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved