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 A000524 Number of rooted trees with n nodes, 2 of which are labeled. (Formerly M1927 N0761) 12
 2, 9, 34, 119, 401, 1316, 4247, 13532, 42712, 133816, 416770, 1291731, 3987444, 12266845, 37627230, 115125955, 351467506, 1070908135, 3257389088, 9892759091, 30002923380, 90879555521, 274963755791, 831064788976 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 134. 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 FORMULA G.f.: A(x) = B(x)^3+2*B(x)^2 where B(x) is g.f. of A000107. G.f.: A(x) = B(x)^2*(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 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*(2-B(n-1))/(1-B(n-1))^3, x=0, n+1), x, n): seq(a(n), n=2..25); # 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*((2 - B[n-1])/ (1 - B[n-1])^3), {x, 0, n+1}], x, n]; Table[a[n], {n, 2, 25}] (* Jean-François Alcover, Dec 20 2012, translated from Alois P. Heinz's Maple program *) CROSSREFS Cf. A000081, A000107, A000243, A000269, A000444, A000485, A000525, A000526. Sequence in context: A301868 A288958 A212348 * A289614 A120989 A280309 Adjacent sequences:  A000521 A000522 A000523 * A000525 A000526 A000527 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 January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)