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A301470
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Signed recurrence over enriched r-trees: a(n) = (-1)^n + Sum_y Product_{i in y} a(y) where the sum is over all integer partitions of n - 1.
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4
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1, 0, 1, 0, 1, 1, 2, 3, 5, 9, 15, 27, 47, 87, 155, 288, 524, 983, 1813, 3434, 6396, 12174, 22891, 43810, 82925, 159432, 303559, 585966, 1121446, 2171341, 4172932, 8106485, 15635332, 30445899, 58925280, 115014681, 223210718, 436603718, 849480835, 1664740873
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OFFSET
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0,7
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..3266
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FORMULA
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O.g.f.: 1/(1 + x) + x Product_{i > 0} 1/(1 - a(i) x^i).
a(n) = Sum_t (-1)^w(t) where the sum is over all enriched r-trees of size n and w(t) is the sum of leaves of t.
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i<1, 0, b(n, i-1)+a(i)*b(n-i, min(n-i, i))))
end:
a:= n-> `if`(n<2, 1-n, b(n-2$2)+b(n-1, n-2)):
seq(a(n), n=0..45); # Alois P. Heinz, Jun 23 2018
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MATHEMATICA
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a[n_]:=a[n]=(-1)^n+Sum[Times@@a/@y, {y, IntegerPartitions[n-1]}];
Array[a, 30]
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CROSSREFS
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Cf. A032305, A055277, A093637, A127524, A196545, A220418, A273866, A273873, A289501, A290261, A290971, A301342-A301345, A301364-A301368, A301422, A301462, A301467, A301469.
Sequence in context: A307074 A293855 A022858 * A090905 A065956 A328078
Adjacent sequences: A301467 A301468 A301469 * A301471 A301472 A301473
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Mar 21 2018
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STATUS
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approved
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