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A298537
Number of unlabeled rooted trees with n nodes such that every branch of the root has the same number of nodes.
3
1, 1, 2, 3, 6, 10, 25, 49, 127, 291, 766, 1843, 5003, 12487, 34151, 87983, 242088, 634848, 1763749, 4688677, 13085621, 35241441, 98752586, 268282856, 755353825, 2067175933, 5837592853, 16087674276, 45550942142, 126186554309, 358344530763, 997171512999
OFFSET
1,3
LINKS
FORMULA
a(n + 1) = Sum_{d|n} binomial(A000081(n/d) + d - 1, d).
EXAMPLE
The a(5) = 6 trees: ((((o)))), (((oo))), ((o(o))), ((ooo)), ((o)(o)), (oooo).
MATHEMATICA
r[n_]:=r[n]=If[n===1, 1, Sum[Product[Binomial[r[x]+Count[ptn, x]-1, Count[ptn, x]], {x, Union[ptn]}], {ptn, IntegerPartitions[n-1]}]];
Table[If[n===1, 1, Sum[Binomial[r[(n-1)/d]+d-1, d], {d, Divisors[n-1]}]], {n, 40}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 20 2018
STATUS
approved