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 A006081 Number of line-rooted projective plane trees with n nodes. (Formerly M2593) 5
 1, 1, 3, 6, 17, 44, 133, 404, 1319, 4392, 15114, 52796, 187410, 671848, 2430509, 8852584, 32438603, 119463056, 441926206, 1641246060, 6117011262, 22871513128, 85766691938, 322479555096, 1215493792902, 4591852445104, 17383416640308, 65937045017304 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). P. K. Stockmeyer, The charm bracelet problem and its applications, pp. 339-349 of Graphs and Combinatorics (Washington, Jun 1973), Ed. by R. A. Bari and F. Harary. Lect. Notes Math., Vol. 406. Springer-Verlag, 1974. LINKS Alois P. Heinz, Table of n, a(n) for n = 2..1000 P. J. Stockmeyer, The charm bracelet problem and its applications, pp. 339-349 of Graphs and Combinatorics (Washington, Jun 1973), Ed. by R. A. Bari and F. Harary. Lect. Notes Math., Vol. 406. Springer-Verlag, 1974. [Scanned annotated and corrected copy] FORMULA Stockmeyer gives g.f. a(n) ~ 2^(2*n-4) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Sep 12 2014 MAPLE b:= proc(n) option remember; binomial(n, floor(n/2)) end: c:= proc(n) option remember; binomial(2*n, n) /(n+1) end: a:= proc(m) local n; n:=m-2; (add(c(k)*c(n-k) +b(k)*b(n-k), k=0..n)) /4 +`if`(irem(n, 2)=0, c(n/2)/2, 0) end: seq(a(n), n=2..30); # Alois P. Heinz, Feb 03 2009 MATHEMATICA b[n_] := Binomial[n, Floor[n/2]]; c[n_] := Binomial[2n, n]/(n+1); a[m_] := (n = m-2; Sum[c[k]*c[n-k] + b[k]*b[n-k], {k, 0, n}]/4 + If[Mod[n, 2] == 0, c[n/2]/2, 0]); Table[a[n], {n, 2, 30}] (* Jean-François Alcover, Jul 20 2011, after Alois P. Heinz *) CROSSREFS Cf. A000108, A001405. - Alois P. Heinz, Feb 03 2009 Sequence in context: A216878 A237670 A321227 * A099511 A204517 A307685 Adjacent sequences:  A006078 A006079 A006080 * A006082 A006083 A006084 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Alois P. Heinz, Feb 03 2009 STATUS approved

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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)