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A325504 Product of products of parts over all strict integer partitions of n. 12
1, 1, 2, 6, 12, 120, 1440, 40320, 1209600, 1567641600, 2633637888000, 13905608048640000, 5046067048690483200000, 5289893008483207348224000000, 1266933607446134946465526579200000000, 99304891373531545064656621572980736000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..30

FORMULA

A001222(a(n)) = A325515(n).

a(n) = A003963(A325506(n)).

EXAMPLE

The strict partitions of 5 are {(5), (4,1), (3,2)} with product a(5) = 5*4*1*3*2 = 120.

The sequence of terms together with their prime indices begins:

              1: {}

              1: {}

              2: {1}

              6: {1,2}

             12: {1,1,2}

            120: {1,1,1,2,3}

           1440: {1,1,1,1,1,2,2,3}

          40320: {1,1,1,1,1,1,1,2,2,3,4}

        1209600: {1,1,1,1,1,1,1,1,2,2,2,3,3,4}

     1567641600: {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,4}

  2633637888000: {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,4,4}

MAPLE

a:= n-> mul(i, i=map(x-> x[], select(x->

        nops(x)=nops({x[]}), combinat[partition](n)))):

seq(a(n), n=0..15);  # Alois P. Heinz, Aug 03 2021

# second Maple program:

b:= proc(n, i) option remember; `if`(n=0, [1$2], `if`(i<1, [0, 1], ((f, g)->

     [f[1]+g[1], f[2]*g[2]*i^g[1]])(b(n, i-1), b(n-i, min(n-i, i-1)))))

    end:

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

seq(a(n), n=0..15);  # Alois P. Heinz, Aug 03 2021

MATHEMATICA

Table[Times@@Join@@Select[IntegerPartitions[n], UnsameQ@@#&], {n, 0, 10}]

CROSSREFS

Cf. A006128, A007870 (non-strict version), A015723, A022629 (sum of products of parts), A066186, A066189, A066633, A246867, A325505, A325506, A325512, A325513, A325515.

Sequence in context: A193987 A089423 A062349 * A193619 A290406 A319481

Adjacent sequences:  A325501 A325502 A325503 * A325505 A325506 A325507

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 07 2019

STATUS

approved

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Last modified September 24 12:17 EDT 2021. Contains 347642 sequences. (Running on oeis4.)