A300439 Number of odd enriched p-trees of weight n (all outdegrees are odd).

1, 1, 2, 2, 5, 7, 18, 29, 75, 132, 332, 651, 1580, 3268, 7961, 16966, 40709, 89851, 215461, 484064, 1159568, 2641812, 6337448, 14622880, 35051341, 81609747, 196326305, 459909847, 1107083238, 2611592457, 6299122736, 14926657167, 36069213786, 85809507332

Offset

1,3

Comments

An odd enriched p-tree of weight n > 0 is either a single node of weight n, or a finite odd-length sequence of at least 3 odd enriched p-trees whose weights are weakly decreasing and sum to n.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Example

The a(6) = 7 odd enriched p-trees: 6, (411), (321), (222), ((111)21), ((211)11), (21111).

Mathematica

f[n_]:=f[n]=1+Sum[Times@@f/@y, {y, Select[IntegerPartitions[n], Length[#]>1&&OddQ[Length[#]]&]}];
Array[f, 40]

Prog

(PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + polcoef(1/prod(k=1, n-1, 1 - v[k]*x^k + O(x*x^n)) - 1/prod(k=1, n-1, 1 + v[k]*x^k + O(x*x^n)), n)/2); v} \\ Andrew Howroyd, Aug 26 2018

Crossrefs

Cf. A000009, A027193, A063834, A078408, A196545, A273873, A289501, A294079, A298118, A299202, A299203, A300300, A300301, A300436, A300440.

Sequence in context: A079280 A038750 A356434 * A208818 A221835 A074476

Adjacent sequences: A300436 A300437 A300438 * A300440 A300441 A300442

Keyword

nonn

Author

Gus Wiseman, Mar 05 2018

Status

approved