A188490 Exponential transform of A003024, number of acyclic digraphs with n labeled nodes.

1, 1, 2, 10, 146, 6010, 636428, 163326124, 98126803670, 134925234752998, 417644922244986812, 2873459543869519132876, 43497844823465975411261876, 1436705096446765490152625035300, 102817732537500055044863771641124696

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

G.f.: A(x) = exp( Sum_{n>=1} A003024(n)*x^n/n ) where A003024(n) is the number of acyclic digraphs with n labeled nodes.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 146*x^4 + 6010*x^5 +...
log(A(x)) = x + 3*x^2/2 + 25*x^3/3 + 543*x^4/4 + 29281*x^5/5 + 3781503*x^6/6 +...+ A003024(n)*x^n/n +...

Prog

(PARI) {A003024(n)=polcoeff(1-sum(k=0, n-1, A003024(k)*x^k/(1+2^k*x+x*O(x^n))^(k+1)), n)}
{a(n)=polcoeff(exp(sum(m=1, n, A003024(m)*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A003024 (log).

Sequence in context: A137884 A057565 A152804 * A317075 A295207 A213457

Adjacent sequences: A188487 A188488 A188489 * A188491 A188492 A188493

Keyword

nonn

Author

Paul D. Hanna, Apr 01 2011

Status

approved