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A101490
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G.f. satisfies A(x) = x*(1+A^2)^2/(1-A+A^2).
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2
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0, 1, 1, 3, 8, 25, 80, 267, 911, 3170, 11192, 39993, 144320, 525124, 1924196, 7093603, 26288928, 97878831, 365918064, 1372982706, 5168555770, 19514482964, 73876936272, 280363191353, 1066357904128, 4064204607372
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| M. Bousquet-Melou, Limit laws for embedded trees
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 413
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FORMULA
| G.f: x*c(x)*c(x^2*c(x)^2), c(x) the g.f. of A000108. [From Paul Barry, Jun 02 2009]
a(n+1)=Sum_{k, 0<=k<=[n/2]}A039599(n-k,k)*A000108(k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 12 2007
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MATHEMATICA
| m = 26; c[0] = 0; c[1] = 1; c[2] = 1; gf[x_] = Sum[c[k]*x^k, {k, 0, m}]; se = Series[-gf[x] + x*(1 + gf[x]^2)^2/(1 - gf[x] + gf[x]^2), {x, 0, m}]; First[Array[c, m, 0] /. Solve[ Thread[ CoefficientList[se, x] == 0]]]
(* From Jean-François Alcover, Jun 29 2011 *)
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CROSSREFS
| Sequence in context: A060404 A192905 A192207 * A148793 A180718 A197159
Adjacent sequences: A101487 A101488 A101489 * A101491 A101492 A101493
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KEYWORD
| nonn
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AUTHOR
| Ralf Stephan, Jan 21 2005
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