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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
Euler transform of A036249 (as well as first differences thereof). - Franklin T. Adams-Watters, Feb 08 2006
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
First differences of A036249 and A029856.
Sequence in context: A027077 A291243 A153774 * A133787 A080923 A118264
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

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)