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A305572
a(n) = (-1)^(n-1) + Sum_{d|n, d>1} a(n/d)^d.
1
1, 0, 2, 0, 2, 4, 2, 0, 10, 4, 2, 32, 2, 4, 42, 0, 2, 228, 2, 32, 138, 4, 2, 1536, 34, 4, 1514, 32, 2, 3940, 2, 0, 2058, 4, 162, 102944, 2, 4, 8202, 1536, 2, 51940, 2, 32, 207370, 4, 2, 3538944, 130, 3204, 131082, 32, 2, 15668836, 2082, 1536, 524298, 4, 2, 54327840
OFFSET
1,3
LINKS
FORMULA
a(n) = Sum_t (-1)^(n-k) where the sum is over all same-trees of weight n (see A281145 for definition) and k is the number of leaves.
MATHEMATICA
a[n_]:=a[n]=(-1)^(n-1)+Sum[a[n/y]^y, {y, Divisors[n]//Rest}];
Array[a, 40]
PROG
(PARI) A305572(n) = ((-1)^(n-1) + sumdiv(n, d, if(d==1, 0, A305572(n/d)^d))); \\ Antti Karttunen, Dec 05 2021
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 05 2018
STATUS
approved