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A325504 Product of products of parts over all strict integer partitions of n. 10
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

Table of n, a(n) for n=0..15.

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}

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 October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)