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A362169
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a(n) = the hypergraph Catalan number C_4(n).
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7
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1, 1, 70, 15225, 7043750, 6327749750, 10411817136000, 29034031694460625, 126890003304310093750, 816448082514611102718750, 7379204202189710013311562500, 90369225128606332243844280406250, 1457163640851863433667228849319062500, 30217741884769257764596041337071409375000
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OFFSET
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0,3
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COMMENTS
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Let m >= 1. The sequence of hypergraph Catalan numbers {C_m(n): n >= 0} is defined in terms of counting walks on trees, weighted by the orders of their automorphism groups. See Gunnells. When m = 1 we get the sequence of Catalan numbers A000108. The present sequence is the case m = 4.
Gunnells gives several combinatorial interpretations of the hypergraph Catalan numbers, a method to compute their generating functions to arbitrary precision and some conjectural asymptotics.
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LINKS
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FORMULA
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a(n) ~ sqrt(2) * (32/3)^n * n!^3/(Pi*n)^(3/2) (conjectural).
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PROG
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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