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A300384 In the ranked poset of integer partitions ordered by refinement, number of maximal chains from the local minimum to the partition with Heinz number n. 1
0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 11, 2, 2, 1, 33, 1, 116, 1, 5, 4, 435, 1, 2, 11, 1, 2, 1832, 2, 8167, 1, 12, 33, 10, 1, 39700, 116, 37, 1, 201785, 5, 1099449, 4, 3, 435, 6237505, 1, 19, 2, 123, 11, 37406458, 1, 27, 2, 474, 1832, 232176847, 2, 1513796040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

The a(21) = 5 maximal chains are the rows:

(111111)<(21111)<(2211)<(222)<(42)

(111111)<(21111)<(2211)<(411)<(42)

(111111)<(21111)<(2211)<(321)<(42)

(111111)<(21111)<(3111)<(411)<(42)

(111111)<(21111)<(3111)<(321)<(42)

MATHEMATICA

pcovs[ptn_]:=Select[Union[Reverse/@Sort/@Join@@@Tuples[IntegerPartitions/@ptn]], Length[#]===Length[ptn]+1&];

coc[ptn_]:=coc[ptn]=If[Max[ptn]===1, 1, Total[coc/@pcovs[ptn]]];

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Table[coc[Reverse[primeMS[n]]], {n, 50}]

CROSSREFS

Cf. A000041, A001055, A001222, A002846, A056239, A112798, A213427, A215366, A265947, A296150, A299200, A299202, A299925, A300273, A300383, A300385.

Sequence in context: A112331 A133910 A066441 * A252890 A173398 A104404

Adjacent sequences:  A300381 A300382 A300383 * A300385 A300386 A300387

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 04 2018

STATUS

approved

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Last modified June 24 05:21 EDT 2019. Contains 324318 sequences. (Running on oeis4.)