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A301751 Number of ways to choose a rooted partition of each part in a strict rooted partition of n. 2
1, 1, 1, 3, 5, 10, 17, 32, 54, 100, 166, 289, 494, 840, 1393, 2400, 3931, 6498, 10861, 17728, 28863, 47557, 77042, 123881, 201172, 322459, 517032, 827993, 1316064, 2084632, 3328204, 5236828, 8247676, 13005652, 20417628, 31934709, 49970815, 77789059, 121144373 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A rooted partition of n is an integer partition of n - 1.

LINKS

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

FORMULA

O.g.f.: x * Product_{n > 0} (1 + A000041(n-1) x^n).

EXAMPLE

The a(7) = 17 rooted twice-partitions:

(5), (41), (32), (311), (221), (2111), (11111),

(4)(), (31)(), (22)(), (211)(), (1111)(), (3)(1), (21)(1), (111)(1),

(2)(1)(), (11)(1)().

MATHEMATICA

nn=50;

ser=x*Product[1+PartitionsP[n-1]x^n, {n, nn}];

Table[SeriesCoefficient[ser, {x, 0, n}], {n, nn}]

PROG

(PARI) seq(n)={Vec(prod(k=1, n-1, 1 + numbpart(k-1)*x^k + O(x^n)))} \\ Andrew Howroyd, Aug 29 2018

CROSSREFS

Cf. A002865, A032305, A063834, A093637, A271619, A281113, A296118, A300383, A301422, A301462, A301467, A301480, A301706.

Sequence in context: A005403 A018072 A090170 * A054166 A265317 A054157

Adjacent sequences:  A301748 A301749 A301750 * A301752 A301753 A301754

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 26 2018

STATUS

approved

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Last modified August 10 20:21 EDT 2022. Contains 356039 sequences. (Running on oeis4.)