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A160564
Sum of products of factorials of parts times the factorial of the number of parts in all integer partitions of n.
1
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
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
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, May 19 2009
STATUS
approved