A205500 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/n * Product_{d|n} A(d*x^n)^d ).

1, 1, 2, 4, 11, 24, 73, 171, 500, 1276, 3698, 9588, 28119, 75094, 217835, 599077, 1736639, 4842231, 14092249, 39844806, 116011719, 331986975, 969188079, 2796468133, 8188982136, 23798219204, 69884802788, 204303838580, 601666227876, 1767334874977, 5219585473815

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 11*x^4 + 24*x^5 + 73*x^6 + 171*x^7 +...
By definition:
log(A(x)) = x*A(x) + x^2*A(x^2)*A(2*x^2)^2/2 + x^3*A(x^3)*A(3*x^3)^3/3 + x^4*A(x^4)*A(2*x^4)^2*A(4*x^4)^4/4 + x^5*A(x^5)*A(5*x^5)^5/5 + x^6*A(x^6)*A(2*x^6)^2*A(3*x^6)^3*A(6*x^6)^6/6 +...
Explicitly,
log(A(x)) = x + 3*x^2/2 + 7*x^3/3 + 27*x^4/4 + 56*x^5/5 + 243*x^6/6 + 512*x^7/7 + 1923*x^8/8 + 4777*x^9/9 +...

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^d, x, d*x^m +x*O(x^n)))))))); polcoeff(A, n)}

Crossrefs

Cf. A205498, A205499, A205501, A205502.

Sequence in context: A183510 A230984 A196195 * A342533 A131434 A100550

Adjacent sequences: A205497 A205498 A205499 * A205501 A205502 A205503

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved