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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.) 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
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.
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
KEYWORD
nonn
AUTHOR
Christian G. Bower, Nov 15 1998
STATUS
approved

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