

A052855


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


4



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
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OFFSET

0,3


COMMENTS

Euler transform of A036249 (as well as first differences thereof).  Franklin T. AdamsWatters, 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)/(1x^n) * x^n/n ). [From Paul D. Hanna, Oct 26 2011]


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] (* JeanFrançois Alcover, May 25 2018 *)


PROG

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


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. AdamsWatters, Feb 08 2006


STATUS

approved



