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A000314
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Number of mixed Husimi trees with n nodes; or labeled polygonal cacti with bridges.
(Formerly M3639 N1480)
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12
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1, 1, 1, 4, 31, 362, 5676, 111982, 2666392, 74433564, 2384579440, 86248530296, 3476794472064, 154579941792256, 7514932528712896, 396595845237540600, 22581060079942183936, 1379771773100463174608, 90059660791562688208128, 6253914166368448348512064
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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REFERENCES
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G. W. Ford and G. E. Uhlenbeck, Combinatorial problems in the theory of graphs III, Proc. Nat. Acad. Sci. USA, 42 (1956), 529-535.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..100
Index entries for sequences related to cacti
Index entries for sequences related to trees
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FORMULA
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a(n) = A035351/n, n>0.
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MAPLE
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A:= proc(n) option remember; if n<=0 then x else convert (series (x* exp ((2*A(n-1) -A(n-1)^2)/ (2-2*A(n-1))), x=0, n+2), polynom) fi end: a:= n-> if n=0 then 1 else coeff (series (A(n-1), x=0, n+1), x, n)*(n-1)! fi: seq (a(n), n=0..30); # Alois P. Heinz, Aug 20 2008
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CROSSREFS
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Cf. A000083, A000237, A035082, A035349-A035357.
Sequence in context: A201628 A086677 A016036 * A128709 A138860 A198865
Adjacent sequences: A000311 A000312 A000313 * A000315 A000316 A000317
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms and formula from Christian G. Bower, Nov 15 1998
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STATUS
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approved
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