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A301470 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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..3266

FORMULA

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.

MAPLE

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

MATHEMATICA

a[n_]:=a[n]=(-1)^n+Sum[Times@@a/@y, {y, IntegerPartitions[n-1]}];

Array[a, 30]

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 21 2018

STATUS

approved

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Last modified April 12 15:00 EDT 2021. Contains 342921 sequences. (Running on oeis4.)