A187847 Number of permutations p of [n] with p(i) <> i^2.
1, 0, 1, 4, 14, 78, 504, 3720, 30960, 256320, 2656080, 30078720, 369774720, 4906137600, 69894316800, 1064341555200, 16190733081600, 279499828608000, 5100017213491200, 98087346669312000, 1983334021853184000, 42063950934061056000, 933754193111900160000
Offset: 0
Keywords
Examples
a(3) = 4: (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1).
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..200
Programs
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Maple
with(LinearAlgebra): a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> `if`(j<>i^2, 1, 0)))): seq(a(n), n=0..15); # second Maple program: a:= n->(p->add((-1)^(j)*binomial(p, j)*(n-j)!, j=0..p))(floor(sqrt(n))): seq(a(n), n=0..25); # Alois P. Heinz, Nov 02 2014
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Mathematica
a[n_] := With[{p = Floor[Sqrt[n]]}, Sum[(-1)^j*Binomial[p, j]*(n-j)!, {j, 0, p}]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 25}] (* Jean-François Alcover, Jan 07 2016, adapted from Maple *)
Formula
a(n) = Sum_{j=0..floor(sqrt(n))} (-1)^j*C(floor(sqrt(n)),j)*(n-j)!.
Comments