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A052827
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A simple grammar.
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0
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1, 1, 1, 3, 6, 15, 36, 90, 225, 578, 1492, 3901, 10278, 27313, 73042, 196585, 531847, 1445991, 3948282, 10823524, 29776129, 82183115, 227501127, 631494797, 1757297207, 4901491697, 13700742034, 38373104938, 107675540083, 302664162746
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 792
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FORMULA
| G.f.: Product_{k>0} (1+x^k)^A000081(k), k=1..infinity). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 14 2005
G.f.: A(x) = x*T(x)/T(x^2) = exp(T(x) - T(x^2)/2 + T(x^3)/3 - T(x^4)/4 +-...) where T(x) = g.f. of A000081 (number of rooted trees with n nodes). - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 13 2006
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EXAMPLE
| A(x) = 1 + x + x^2 + 3*x^3 + 6*x^4 + 15*x^5 + 36*x^6 + 90*x^7 +...
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MAPLE
| spec := [S, {B=Set(C), C=Prod(B, Z), S=PowerSet(C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROG
| (PARI) {a(n)=local(T=x+x*O(x^n)); if(n==0, 1, for(i=1, n, T=x*exp(sum(k=1, n, subst(T, x, x^k+x*O(x^n))/k))); polcoeff(x*T/subst(T, x, x^2), n, x))} - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 13 2006
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CROSSREFS
| Cf. A000081.
Sequence in context: A190586 A113225 A017924 * A033192 A174297 A005043
Adjacent sequences: A052824 A052825 A052826 * A052828 A052829 A052830
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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 Paul D. Hanna (pauldhanna(AT)juno.com), Jul 13 2006
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