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A266480 Maximal product of multiplicities of parts of a partition of n. 4
1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 15, 18, 21, 24, 28, 32, 36, 40, 45, 50, 56, 64, 72, 84, 96, 108, 120, 135, 150, 165, 180, 200, 220, 240, 264, 288, 312, 336, 364, 405, 450, 495, 540, 600, 660, 720, 792, 864, 936, 1008, 1092, 1176, 1260, 1365, 1470, 1575 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..16000 (terms 0..5000 from Alois P. Heinz)

EXAMPLE

a(4) = 4 because the products of the multiplicities of the parts in the partitions [4], [1,3], [2,2], [1,1,2], [1,1,1,1] are 1, 1, 2, 2, 4, respectively.

a(21) = 7*4*2 = 56 for partition [1,1,1,1,1,1,1,2,2,2,2,3,3].

MAPLE

b:= proc(n, i) option remember; `if`(n=0 or i=1, max(1, n),

      max(seq(b(n-i*j, i-1)*max(1, j), j=0..n/i)))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..100);

MATHEMATICA

Table[Max@ Map[Times @@ Map[Last, Tally@ #] &, IntegerPartitions@ n], {n, 0, 56}] (* Michael De Vlieger, Dec 31 2015 *)

b[n_, i_] := b[n, i] = If[n==0 || i==1, Max[1, n], Max[Table[b[n-i*j, i-1]*Max[1, j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Sep 01 2016, after Alois P. Heinz *)

CROSSREFS

Row lengths of A266477.

Cf. A266871.

Sequence in context: A003045 A279079 A029750 * A246080 A278619 A173925

Adjacent sequences:  A266477 A266478 A266479 * A266481 A266482 A266483

KEYWORD

nonn

AUTHOR

Emeric Deutsch and Alois P. Heinz, Dec 29 2015

STATUS

approved

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Last modified September 25 18:27 EDT 2022. Contains 356986 sequences. (Running on oeis4.)