A160564 Sum of products of factorials of parts times the factorial of the number of parts in all integer partitions of n.

1, 1, 4, 16, 80, 420, 2592, 17352, 132240, 1117200, 10559040, 110276352, 1268640000, 15923168640, 216767367936, 3178157607936, 49918919122944, 835744605027840, 14852897362759680, 279172076525153280, 5531978038112409600, 115241366146485749760

Offset

0,3

Comments

Take each Ferrers diagram of the partitions of n, label the cells within each row and then linearly order the rows.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Example

a(3) = 16 because the partitions of 3 can be so ordered in 16 ways: 3 (6); 2,1 (4); 1,1,1 (6).

Maple

b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(b(n-i*j, i-1, p+j)*i!^j, j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..23);  # Alois P. Heinz, Oct 02 2017

Mathematica

p = Table[Map[Function[n, Apply[Times, n! ]], Partitions[i]], {i, 0, 20}]; q = Table[Map[Function[n, Length[n]! ], Partitions[i]], {i, 0, 20}]; Map[Function[n, Apply[Plus, n]], p*q]

Crossrefs

Cf. A101880, A077365, A126787.

Sequence in context: A094013 A106568 A183146 * A075581 A171454 A316944

Adjacent sequences: A160561 A160562 A160563 * A160565 A160566 A160567

Keyword

nonn

Author

Geoffrey Critzer, May 19 2009

Status

approved