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A321467 Number of factorizations of n! into factors > 1 that can be obtained by taking the block-products of some set partition of {2,3,...,n}. 5
1, 1, 1, 2, 5, 15, 47, 183, 719, 3329, 14990, 83798, 393864, 2518898 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) is the number of factorizations coarser than (2*3*...*n) in the poset of factorizations of n! into factors > 1, ordered by refinement.

LINKS

Table of n, a(n) for n=0..13.

EXAMPLE

The a(1) = 1 through a(5) = 15 factorizations:

  ()  (2)  (6)    (24)     (120)

           (2*3)  (3*8)    (2*60)

                  (4*6)    (3*40)

                  (2*12)   (4*30)

                  (2*3*4)  (5*24)

                           (6*20)

                           (8*15)

                           (10*12)

                           (3*5*8)

                           (4*5*6)

                           (2*3*20)

                           (2*4*15)

                           (2*5*12)

                           (3*4*10)

                           (2*3*4*5)

For example, 10*12 = (2*5)*(3*4), so (10*12) is counted under a(5).

MATHEMATICA

sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];

Table[Length[Union[Sort/@Apply[Times, sps[Range[2, n]], {2}]]], {n, 10}]

CROSSREFS

Dominated by A000110.

Cf. A001055, A066723, A157612, A242422, A265947, A317141, A317144, A317145, A317534, A321468, A321470, A321471, A321472, A321514.

Sequence in context: A149924 A149925 A149926 * A301994 A289589 A071739

Adjacent sequences:  A321464 A321465 A321466 * A321468 A321469 A321470

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 11 2018

STATUS

approved

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Last modified January 24 08:48 EST 2022. Contains 350534 sequences. (Running on oeis4.)