A052855 Number of forests of rooted trees of nonempty sets with n points. (Each node is a set of 1 or more points.)

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

Offset

0,3

Comments

Euler transform of A036249 (as well as first differences thereof). - Franklin T. Adams-Watters, Feb 08 2006

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 823

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

First differences of A036249 and A029856.

Sequence in context: A027077 A291243 A153774 * A133787 A080923 A118264

Adjacent sequences: A052852 A052853 A052854 * A052856 A052857 A052858

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

More terms from Franklin T. Adams-Watters, Feb 08 2006

Status

approved