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A055544
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Total number of nodes in all rooted trees with n nodes.
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6
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x * (d/dx) x * Product_{k>=1} 1/(1 - x^k)^(a(k)/k). - Ilya Gutkovskiy, May 26 2019
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MAPLE
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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):
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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