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 A242375 Number of rooted trees with n n-colored non-root nodes. 3
 1, 1, 7, 82, 1499, 37476, 1200705, 46990952, 2175619923, 116400215521, 7069820334023, 480722969498938, 36186340018129392, 2987845924408179654, 268530017303221572650, 26098422892000807053155, 2727654868575748827350403, 305075571192329680642519141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA a(n) ~ c * exp(n) * n^(n-3/2), where c = 1.160358615244339554387715747... . - Vaclav Kotesovec, Aug 28 2014 EXAMPLE a(2) = 7: o o o o o o o | | | | / \ / \ / \ 1 1 2 2 1 1 1 2 2 2 | | | | 1 2 1 2 MAPLE with(numtheory): b:= proc(n, k) option remember; `if`(n<2, n, (add(add(d* b(d, k), d=divisors(j))*b(n-j, k)*k, j=1..n-1))/(n-1)) end: a:= n-> b(n+1, n): seq(a(n), n=0..20); MATHEMATICA b[n_, k_] := b[n, k] = If[n < 2, n, (Sum[Sum[d*b[d, k], {d, Divisors[j]}] * b[n - j, k]*k, {j, 1, n - 1}])/(n - 1)]; a[n_] := b[n + 1, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 21 2017, translated from Maple *) CROSSREFS A diagonal of A242249. Cf. A255523. Sequence in context: A191804 A243672 A268653 * A333984 A244821 A304591 Adjacent sequences: A242372 A242373 A242374 * A242376 A242377 A242378 KEYWORD nonn AUTHOR Alois P. Heinz, May 12 2014 STATUS approved

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Last modified December 5 21:40 EST 2022. Contains 358594 sequences. (Running on oeis4.)