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A036249 Number of rooted trees of nonempty sets with n points. (Each node is a set of 1 or more points.) 8
0, 1, 2, 5, 13, 37, 108, 332, 1042, 3360, 11019, 36722, 123875, 422449, 1453553, 5040816, 17599468, 61814275, 218252584, 774226549, 2758043727, 9862357697, 35387662266, 127374191687, 459783039109, 1664042970924, 6037070913558, 21951214425140, 79981665585029 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1717

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.

F. Chapoton, F. Hivert, J.-C. Novelli, A set-operad of formal fractions and dendriform-like sub-operads, Journal of Algebra, 465 (2016), 322-355.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 768

Index entries for sequences related to rooted trees

FORMULA

G.f. satisfies: A(x) = x*exp( Sum_{n>=1} (A(x^n) + x^n)/n ). - Paul D. Hanna, Oct 19 2005

If b(n) is the Euler transform of a(n), A052855, then a(n+1) = a(n) + b(n). - Franklin T. Adams-Watters, Mar 09 2006

MAPLE

b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*

      add(d*a(d), d=numtheory[divisors](j)), j=1..n)/n)

    end:

a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+b(n-1)) end:

seq(a(n), n=0..35);  # Alois P. Heinz, Jun 13 2018

MATHEMATICA

max = 27; A[_] = 1; Do[A[x_] = x*Exp[Sum[(A[x^k] + x^k)/k + O[x]^n, {k, 1, n}]] // Normal, {n, 1, max}]; CoefficientList[A[x] + O[x]^max, x] (* Jean-Fran├žois Alcover, May 25 2018 *)

PROG

(PARI) {a(n)=local(A=x+x*O(x^n)); for(i=1, n, A=x*exp(sum(m=1, n, (subst(A, x, x^m)+x^m)/m))); polcoeff(A, n, x)} \\ Paul D. Hanna, Oct 19 2005

CROSSREFS

Essentially the same as A029856. Cf. A048802. Row sums of A303911.

Sequence in context: A293297 A318485 A005961 * A126031 A151416 A193114

Adjacent sequences:  A036246 A036247 A036248 * A036250 A036251 A036252

KEYWORD

nonn

AUTHOR

Christian G. Bower, Nov 15 1998

STATUS

approved

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Last modified August 10 16:56 EDT 2020. Contains 336381 sequences. (Running on oeis4.)