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A301767 Number of ways to choose a constant rooted partition of each part in a strict rooted partition of n. 1
1, 1, 1, 3, 4, 7, 9, 15, 21, 32, 45, 59, 89, 117, 162, 225, 309, 394, 538, 707, 929, 1240, 1613, 2055, 2677, 3517, 4439, 5724, 7288, 9222, 11671, 14809, 18480, 23226, 29138, 36501, 45373, 56438, 69920, 86426, 106715, 131171, 161428, 197717, 242301, 295888 (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

Table of n, a(n) for n=1..46.

FORMULA

O.g.f.: Product_{n>0} (1 + d(n-1) x^n) where d(n) = A000005(n) and d(0) = 1.

EXAMPLE

The a(7) = 9 rooted twice-partitions:

(5), (11111),

(4)(), (22)(), (1111)(), (3)(1), (111)(1),

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

MATHEMATICA

Table[Sum[Product[If[k===1, 1, DivisorSigma[0, k-1]], {k, ptn}], {ptn, Select[IntegerPartitions[n-1], UnsameQ@@#&]}], {n, 50}]

CROSSREFS

Cf. A002865, A032305, A063834, A093637, A279786, A296131, A301422, A301462, A301467, A301480, A301706.

Sequence in context: A241335 A158911 A086772 * A169898 A281734 A086336

Adjacent sequences:  A301764 A301765 A301766 * A301768 A301769 A301770

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 26 2018

STATUS

approved

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Last modified June 7 02:48 EDT 2020. Contains 334836 sequences. (Running on oeis4.)