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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
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * exp(n) * n^(n-3/2), where c = exp(1 + exp(-2)/2) / sqrt(2*Pi) = 1.160358615244339554387715748... . - Vaclav Kotesovec, Aug 28 2014, updated Mar 18 2024
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: A268653 A364939 A360473 * A333984 A244821 A304591
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 12 2014
STATUS
approved