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A301469 Signed recurrence over enriched r-trees: a(n) = 2 * (-1)^n + Sum_y Product_{i in y} a(y) where the sum is over all integer partitions of n - 1. 3
2, -1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 3, 3, 6, 7, 11, 17, 23, 35, 53, 75, 119, 173, 264, 398, 603, 911, 1411, 2114, 3279, 4977, 7696, 11760, 18253, 27909, 43451, 66675, 103945, 160096, 249904, 385876, 603107, 933474, 1461967, 2266384, 3553167, 5521053, 8664117, 13485744 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..48.

FORMULA

O.g.f.: 2/(1 + x) + x Product_{i > 0} 1/(1 - a(i) x^i).

a(n) = Sum_t 2^k * (-1)^w where the sum is over all enriched r-trees of size n, k is the number of leaves, and w is the sum of leaves.

MATHEMATICA

a[n_]:=a[n]=2(-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, A290973, A301342-A301345, A301364-A301368, A301422, A301462, A301467, A301470.

Sequence in context: A100204 A073779 A081227 * A004610 A068934 A035200

Adjacent sequences:  A301466 A301467 A301468 * A301470 A301471 A301472

KEYWORD

sign

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.)