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A052855
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Number of forests of rooted trees of nonempty sets with n points. (Each node is a set of 1 or more points.)
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Euler transform of A036249 (as well as first differences thereof). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 08 2006
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 823
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FORMULA
| G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x^n)/(1-x^n) * x^n/n ). [From Paul D. Hanna, Oct 26 2011]
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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);
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PROG
| (PARI) {a(n)=local(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 */
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CROSSREFS
| First differences of A036249 and A029856.
Sequence in context: A079121 A027077 A153774 * A133787 A080923 A118264
Adjacent sequences: A052852 A052853 A052854 * A052856 A052857 A052858
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 08 2006
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