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A038037
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Number of labeled rooted compound windmills (mobiles) with n nodes.
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8
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1, 2, 9, 68, 730, 10164, 173838, 3524688, 82627200, 2198295360, 65431163160, 2154106470240, 77714083773456, 3048821300491680, 129221979665461200, 5884296038166954240, 286492923374605966080, 14851359950834255500800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 241 (3.3.83).
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LINKS
| C. G. Bower, Transforms (2)
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 454
Alois P. Heinz, Table of n, a(n) for n = 1..140
Index entries for sequences related to mobiles
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FORMULA
| Divides by n and shifts left under "CIJ" (necklace, indistinct, labeled) transform.
E.g.f. A(x) satisfies A(x)=-x*log(1-A(x)).
a(n) = sum(j=0..n, binomial(n,j) *abs(stirling1(n-1,j))*j!), n>0. [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Feb 03 2011]
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MAPLE
| logtr:= proc(p) local b; b:=proc(n) option remember; local k; if n=0 then 1 else p(n)- add (k *binomial(n, k) *p(n-k) *b(k), k=1..n-1)/n fi end end: b := logtr(-a): a:= n-> `if`(n<=1, 1, -n*b(n-1)): seq (a (n), n=1..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 14 2008]
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MATHEMATICA
| a[n_] = Sum[Binomial[n, j]*Abs[StirlingS1[n-1, j]]*j!, {j, 0, n}]; Array[a, 18]
(* From Jean-François Alcover, Jun 22 2011, after V. Kruchinin *)
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CROSSREFS
| Cf. A029768, A032200, A055349.
Sequence in context: A200248 A180747 A134200 * A138212 A134261 A120980
Adjacent sequences: A038034 A038035 A038036 * A038038 A038039 A038040
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KEYWORD
| nonn,eigen
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Sep 15 1998.
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