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 A052893 Number of objects generated by the Combstruct grammar defined in the Maple program. See the link for the grammar specification. 23
 1, 1, 3, 10, 37, 144, 589, 2483, 10746, 47420, 212668, 966324, 4439540, 20587286, 96237484, 453012296, 2145478716, 10215922013, 48877938369, 234862013473, 1132902329028, 5483947191651, 26630419098206, 129696204701807, 633339363924611, 3100369991303297 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of free pure symmetric multifunctions with n + 1 unlabeled leaves. A free pure symmetric multifunction f in PSM is either (case 1) f = the leaf symbol "o", or (case 2) f = an expression of the form h[g_1, ..., g_k] where k > 0, h is in PSM, each of the g_i for i = 1, ..., k is in PSM, and for i < j we have g_i <= g_j under a canonical total ordering of PSM, such as the Mathematica ordering of expressions. - Gus Wiseman, Aug 02 2018 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 869 Maplesoft, Combstruct grammars. Mathematica Reference, Orderless. FORMULA G.f.: 1/(1 - g(x)) where g(x) is the g.f. of A052891. - Andrew Howroyd, Aug 09 2020 EXAMPLE From Gus Wiseman, Aug 02 2018: (Start) The a(3) = 10 free pure symmetric multifunctions with 4 unlabeled leaves: o[o[o[o]]] o[o[o][o]] o[o][o[o]] o[o[o]][o] o[o][o][o] o[o[o,o]] o[o,o[o]] o[o][o,o] o[o,o][o] o[o,o,o] (End) MAPLE spec := [S, {C = Set(B, 1 <= card), B=Prod(Z, S), S=Sequence(C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20); MATHEMATICA multing[t_, n_]:=Array[(t+#-1)/#&, n, 1, Times]; a[n_]:=a[n]=If[n==1, 1, Sum[a[k]*Sum[Product[multing[a[First[s]], Length[s]], {s, Split[p]}], {p, IntegerPartitions[n-k]}], {k, 1, n-1}]]; Array[a, 30] (* Gus Wiseman, Aug 02 2018 *) PROG (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} seq(n)={my(v=[1]); for(n=1, n, v=Vec(1/(1-x*Ser(EulerT(v))))); v} \\ Andrew Howroyd, Aug 09 2020 CROSSREFS Cf. A001003, A052891, A277996, A279944, A280000. Sequence in context: A264231 A151053 A151054 * A052818 A299501 A226434 Adjacent sequences: A052890 A052891 A052892 * A052894 A052895 A052896 KEYWORD easy,nonn AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 EXTENSIONS More terms from Gus Wiseman, Aug 02 2018 STATUS approved

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Last modified July 24 02:45 EDT 2024. Contains 374575 sequences. (Running on oeis4.)