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A055544 Total number of nodes in all rooted trees with n nodes. 6
1, 2, 6, 16, 45, 120, 336, 920, 2574, 7190, 20262, 57192, 162318, 461622, 1317165, 3766096, 10792399, 30980862, 89084844, 256524560, 739658472, 2135213982, 6170505665, 17849399616, 51679366125, 149750549260, 434260826883, 1260197855532, 3659410074932 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Graph Vertex.
Eric Weisstein's World of Mathematics, Graph Edge
FORMULA
a(n) = n*A000081(n).
G.f.: x * (d/dx) x * Product_{k>=1} 1/(1 - x^k)^(a(k)/k). - Ilya Gutkovskiy, May 26 2019
MAPLE
with(numtheory):
b:= proc(n) option remember; local d, j; `if`(n<2, n,
(add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/ (n-1))
end:
a:= n-> n*b(n):
seq(a(n), n=1..30); # Alois P. Heinz, May 16 2013
MATHEMATICA
b[n_] := b[n] = If[n<2, n, (Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}])/(n-1)]; a[n_] := n*b[n]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Jan 25 2017, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A263897 A209629 A349488 * A126285 A026163 A005717
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 19 03:21 EDT 2024. Contains 370952 sequences. (Running on oeis4.)