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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
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
Sequence in context: A264231 A151053 A151054 * A052818 A299501 A226434
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.)