A205498 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/n * Product_{d|n} A(n*x^d/d) ).

1, 1, 2, 5, 16, 63, 329, 2291, 21986, 293295, 5493212, 145199609, 5435890215, 288986265721, 21854960540507, 2354333160724935, 361635116847622331, 79267245693976433777, 24809117584333459025386, 11092978451251892467436829, 7089163369051891054753027252

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 63*x^5 + 329*x^6 +...
By definition:
log(A(x)) = x*A(x) + x^2*A(2*x)*A(x^2)/2 + x^3*A(3*x)*A(x^3)/3 + x^4*A(4*x)*A(2*x^2)*A(x^4)/4 + x^5*A(5*x)*A(x^5)/5 + x^6*A(6*x)*A(3*x^2)*A(2*x^3)*A(x^6)/6 +...
Explicitly,
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 221*x^5/5 + 1506*x^6/6 + 13196*x^7/7 + 153979*x^8/8 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n+1, x^m/m*exp(sumdiv(m, d, log(subst(A, x, m*x^d/d +x*O(x^n)))))))); polcoeff(A, n)}

Crossrefs

Cf. A205499, A205500, A205501, A205502.

Sequence in context: A079566 A059685 A000112 * A295131 A178119 A185998

Adjacent sequences: A205495 A205496 A205497 * A205499 A205500 A205501

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved