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 A000269 Number of trees with n nodes, 3 of which are labeled. (Formerly M3014 N1220) 9
 3, 16, 67, 251, 888, 3023, 10038, 32722, 105228, 334836, 1056611, 3311784, 10322791, 32026810, 98974177, 304835956, 936147219, 2867586542, 8764280567, 26733395986, 81399821915, 247459136331, 751211286356, 2277496842016 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 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=3..200 FORMULA G.f.: A(x) = B(x)^3*(3-2*B(x))/(1-B(x))^3, where B(x) is g.f. for rooted trees with n nodes, cf. A000081. - Vladeta Jovovic, Oct 19 2001 a(n) = A000524(n) - 2*A000243(n). 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_] := SeriesCoefficient[ B[n-1]^3 * (2*B[n-1]-3) / (B[n-1]-1)^3, {x, 0, n}]; Table[a[n], {n, 3, 30}] (* Jean-François Alcover, Jan 27 2015 *) CROSSREFS Cf. A000055, A000107, A000243, A000444, A000485, A000524, A000525, A000526. Sequence in context: A179600 A278089 A248016 * A015524 A012279 A037098 Adjacent sequences:  A000266 A000267 A000268 * A000270 A000271 A000272 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms, new description and formula from Christian G. Bower, Nov 15 1999 STATUS approved

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Last modified December 10 00:30 EST 2018. Contains 318032 sequences. (Running on oeis4.)