The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A036249 Number of rooted trees of nonempty sets with n points. (Each node is a set of 1 or more points.) 14
 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 G.f.: (x/(1 - x)) * Product_{n>=1} 1/(1 - x^n)^a(n). - Ilya Gutkovskiy, Jun 28 2021 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-François 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 23 11:40 EST 2024. Contains 370283 sequences. (Running on oeis4.)