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 A000243 Number of trees with n nodes, 2 of which are labeled. (Formerly M2803 N1128) 15
 1, 3, 9, 26, 75, 214, 612, 1747, 4995, 14294, 40967, 117560, 337830, 972027, 2800210, 8075889, 23315775, 67380458, 194901273, 564239262, 1634763697, 4739866803, 13752309730, 39926751310, 115988095896, 337138003197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 138. 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). LINKS T. D. Noe, Table of n, a(n) for n=2..200 R. J. Mathar, Topologically distinct sets of non-intersecting circles in the plane, arXiv:1603.00077 [math.CO] (2016), Table 5. FORMULA a(n) = A000107(n) - A000081(n). - Christian G. Bower, Nov 15 1999 G.f.: A(x) = B(x)^2/(1-B(x)), where B(x) is g.f. for rooted trees with n nodes, cf. A000081. - Vladeta Jovovic, Oct 19 2001 a(n) = A000106(n) + A304068(n). - Brendan McKay, May 05 2018 MAPLE b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember; add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember; add(b(k)*x^k, k=1..n) end: a:= n-> coeff(series(B(n-1)^2/(1-B(n-1)), x=0, n+1), x, n): seq(a(n), n=2..27); # Alois P. Heinz, Aug 21 2008 MATHEMATICA b[n_] := b[n] = If[ n <= 1 , n, Sum[k*b[k]*s[n - 1, k], {k, 1, n - 1}]/(n - 1) ]; s[n_, k_] := s[n, k] = Sum[ b[n + 1 - j*k], {j, 1, Quotient[n, k]}]; B[n_] := B[n] = Sum[ b[k]*x^k, {k, 1, n}]; a[n_] := Coefficient[ Series[ B[n - 1]^2/(1 - B[n - 1]), {x, 0, n + 1}], x, n]; Table[ a[n], {n, 2, 27}] (* Jean-François Alcover, Jan 25 2012, translated from Maple *) CROSSREFS Cf. A000055, A000081, A000269, A000485, A000526, A000107, A000524, A000444, A000525. Sequence in context: A171277 A289806 A303976 * A076264 A018919 A123941 Adjacent sequences:  A000240 A000241 A000242 * A000244 A000245 A000246 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms and new description from Christian G. Bower, Nov 15 1999 STATUS approved

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Last modified November 23 14:26 EST 2020. Contains 338590 sequences. (Running on oeis4.)