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A032035
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Number of increasing rooted 2,3 cacti (triangular cacti with bridges) with n-1 nodes.
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1
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1, 1, 1, 3, 13, 77, 573, 5143, 54025, 650121, 8817001, 133049339, 2210979381, 40118485237, 789221836741, 16730904387183, 380227386482641, 9221550336940241, 237724953543108753, 6491255423787076915
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Also increasing involution rooted trees with n-1 nodes.
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LINKS
| C. G. Bower, Transforms (2)
Index entries for sequences related to cacti
Index entries for sequences related to rooted trees
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FORMULA
| E.g.f. of a(n+1) satisfies A'(x) = exp(A(x)+A(x)^2/2)
E.g.f. satisfies A''(x) = 1/(1-A(x)).
Shifts left 2 places under "AIJ" (ordered, indistinct, labeled) transform.
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MAPLE
| A:= proc(n) option remember; if n=0 then x else convert (series (Int (exp (A(n-1)+ A(n-1)^2/2), x), x=0, n+1), polynom) fi end; a:= n-> if n=1 then 1 else coeff (A(n-1), x, n-1)*(n-1)! fi: seq (a(n), n=1..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 22 2008]
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CROSSREFS
| Cf. A001147, A091481.
Sequence in context: A189239 A074530 A159662 * A127127 A043301 A141762
Adjacent sequences: A032032 A032033 A032034 * A032036 A032037 A032038
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KEYWORD
| nonn,eigen
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Apr 01, 1998
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