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A256070
Number of inequivalent n X n matrices with entry set {1,...,n}, where equivalence means permutations of rows or columns.
3
1, 1, 5, 633, 7520386, 20435529209470, 19740907671252532135134, 10077866175951324796988844418739012, 3855174405512686506030123555473042980898031518176, 1492231601551989489818761885384738502799149242563553845787532236092
OFFSET
0,3
FORMULA
a(n) = Sum_{i=0..n} (-1)^i * C(n,i) * A246106(n,n-i).
EXAMPLE
a(2) = 5:
[1 1] [1 2] [1 2] [1 1] [1 2]
[1 2] [2 2] [1 2] [2 2] [2 1].
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [[]],
`if`(i<1, [], [b(n, i-1)[], seq(map(p->[p[], [i, j]],
b(n-i*j, i-1))[], j=1..n/i)]))
end:
A:= proc(n, k) option remember; add(add(k^add(add(i[2]*j[2]*
igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)
/mul(i[1]^i[2]*i[2]!, i=t), t=b(n$2)), s=b(n$2))
end:
a:= n-> add(A(n, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..10);
CROSSREFS
Main diagonal of A256069.
Sequence in context: A209589 A060758 A348081 * A203339 A253690 A068421
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 13 2015
STATUS
approved