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 A174145 Number of rooted forests with n nodes in which each component contains at least two nodes. 4
 1, 0, 1, 2, 5, 11, 28, 67, 171, 433, 1123, 2924, 7720, 20487, 54838, 147570, 399466, 1086312, 2967517, 8137552, 22395604, 61833349, 171227674, 475442129, 1323449661, 3692461865, 10324097819, 28923331940, 81179488039, 228240293289, 642744665401, 1812762839702 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Row sums of A174135. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) ~ c * d^n / n^(3/2), where d = A051491 = 2.9557652856519949747148..., c = 0.8603881121111431... . - Vaclav Kotesovec, Sep 10 2014 In the asymptotics above the constant c = A187770 * (A051491 - 1). - Vladimir Reshetnikov, Aug 12 2016 a(n) = A000081(n+1) - A000081(n). - Vladimir Reshetnikov, Nov 06 2015 MAPLE with(numtheory): t:= proc(n) option remember; local d, j; `if`(n<=1, n,       (add(add(d*t(d), d=divisors(j))*t(n-j), j=1..n-1))/(n-1))     end: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<2, 0,       add(b(n-i*j, i-1)*binomial(t(i)+j-1, j), j=0..n/i)))     end: a:= n-> b(n, n): seq(a(n), n=0..32);  # Alois P. Heinz, May 17 2013 MATHEMATICA t[n_] := t[n] = If[n <= 1, n, Sum[Sum[d*t[d], {d, Divisors[j]}]*t[n-j], {j, 1, n-1}]/(n-1)]; b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<2, 0, Sum[b[n-i*j, i-1]*Binomial[t[i]+j-1, j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n] // FullSimplify, {n, 0, 32}] (* Jean-François Alcover, Mar 19 2014, after Alois P. Heinz *) t[1] = 1; t[n_] := t[n] = Sum[k t[k] t[n - k m]/(n-1), {k, n-1}, {m, (n-1)/k}]; a[n_] := t[n+1] - t[n]; Table[a[n], {n, 0, 32}] (* Vladimir Reshetnikov, Aug 12 2016 *) CROSSREFS Cf. A000081, A051491, A187770, A255170. Sequence in context: A055227 A325916 A257790 * A124016 A121398 A000625 Adjacent sequences:  A174142 A174143 A174144 * A174146 A174147 A174148 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 26 2010 STATUS approved

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Last modified September 24 11:57 EDT 2021. Contains 347642 sequences. (Running on oeis4.)