A300863 Signed recurrence over enriched p-trees: a(n) = (-1)^(n - 1) + Sum_{y1 + ... + yk = n, y1 >= ... >= yk > 0, k > 1} a(y1) * ... * a(yk).

1, 0, 2, 2, 6, 14, 34, 82, 214, 566, 1482, 4058, 10950, 30406, 83786, 235714, 658286, 1874254, 5293674, 15189810, 43312542, 125075238, 359185586, 1043712922, 3015569582, 8800146182, 25565402802, 74918274562, 218572345718, 642783954238, 1882606578002

Offset: 1

Author

Gus Wiseman, Mar 13 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000992, A063834, A099323, A196545, A220418, A273866, A273873, A289501, A290261, A300862, A300864, A300865, A300866.

Programs

Mathematica

a[n_]:=a[n]=(-1)^(n-1)+Sum[Times@@a/@y,{y,Select[IntegerPartitions[n],Length[#]>1&]}];
Array[a,40]

Formula

O.g.f.: (-1/(1+x) + Product 1/(1-a(n)x^n))/2.