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A048802 Number of labeled rooted trees of nonempty sets with n points. (Each node is a set of 1 or more points.) 8
1, 3, 16, 133, 1521, 22184, 393681, 8233803, 198342718, 5408091155, 164658043397, 5537255169582, 203840528337291, 8153112960102283, 352079321494938344, 16325961781591781401, 809073412162081974237, 42674870241038732398720, 2386963662244981472850709 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

F. Chapoton, F. Hivert, J.-C. Novelli, A set-operad of formal fractions and dendriform-like sub-operads, arXiv preprint arXiv:1307.0092 [math.CO], 2013.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 861

B. R. Jones, On tree hook length formulas, Feynman rules and B-series, Master's thesis, Simon Fraser University, 2014.

Index entries for sequences related to rooted trees

FORMULA

E.g.f.: B(exp(x)-1) where B is e.g.f. of A000169.

E.g.f.: Series_Reversion( log(1 + x*exp(-x)) ). - Paul D. Hanna, Jan 24 2016

a(n) = Sum_{k=1..n} Stirling2(n, k)*k^(k-1). - Vladeta Jovovic, Sep 17 2003

Stirling transform of A000169. - Michael Somos, Jun 09 2012

a(n) ~ sqrt(1+exp(1)) * n^(n-1) / (exp(n) * (log(1+exp(-1)))^(n-1/2)). - Vaclav Kotesovec, Feb 17 2014

EXAMPLE

G.f. = x + 3*x^2 + 16*x^3 + 133*x^4 + 1521*x^5 + 22184*x^6 + 393681*x^7 + ...

MATHEMATICA

nn=20; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0, nn]!CoefficientList[ ComposeSeries[ Series[t, {x, 0, nn}], Series[Exp[x]-1 , {x, 0, nn}]], x]  (* Geoffrey Critzer, Sep 16 2012 *)

PROG

(PARI) {a(n) = sum( k=1, n, stirling(n, k, 2) * k^(k - 1))}; /* Michael Somos, Jun 09 2012 */

(PARI) {a(n) = n! * polcoeff( serreverse( log(1 + x*exp(-x +x*O(x^n))) ), n)}

for(n=1, 30, print1(a(n), ", ")) \\ Paul D. Hanna, Jan 24 2016

CROSSREFS

Cf. A036249, A038052, A058863, A052807.

Sequence in context: A023998 A241464 A141628 * A213357 A119392 A307979

Adjacent sequences:  A048799 A048800 A048801 * A048803 A048804 A048805

KEYWORD

nonn

AUTHOR

Christian G. Bower, Mar 15 1999

STATUS

approved

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Last modified December 5 10:45 EST 2019. Contains 329751 sequences. (Running on oeis4.)