|
|
A052855
|
|
Number of forests of rooted trees of nonempty sets with n points. (Each node is a set of 1 or more points.)
|
|
11
|
|
|
1, 1, 3, 8, 24, 71, 224, 710, 2318, 7659, 25703, 87153, 298574, 1031104, 3587263, 12558652, 44214807, 156438309, 555973965, 1983817178, 7104313970, 25525304569, 91986529421, 332408847422, 1204259931815, 4373027942634, 15914143511582, 58030451159889
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
G.f. satisfies A(x) = exp( Sum_{n>=1} A(x^n)/(1-x^n) * x^n/n ). - Paul D. Hanna, Oct 26 2011
G.f.: A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{j>=1} Product_{k>=0} (1-x^(j+k))^a(k). - Seiichi Manyama, Jun 07 2023
|
|
MAPLE
|
spec := [S, {B=Sequence(Z, 1 <= card), S=Set(C), C=Prod(B, S)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
|
|
MATHEMATICA
|
max = 26; A[_] = 1; Do[A[x_] = Exp[Sum[A[x^k]/(1 - 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)=my(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A/(1-x), x, x^m+x*O(x^n))*x^m/m))); polcoeff(A, n)} /* Paul D. Hanna, Oct 26 2011 */
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|