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A369796
Number of permutations of [n] whose fixed points sum to n.
2
1, 1, 0, 1, 3, 13, 64, 406, 2737, 23044, 200509, 2078460, 22323513, 275402437, 3501602483, 50310672046, 739235942264, 12084285146335, 202054808987101, 3703410393626031, 69269248667062892, 1409725495837854024, 29169764518508360709, 651568557906956269430
OFFSET
0,5
LINKS
Wikipedia, Permutation
FORMULA
a(n) = Sum_{k>=0} A000166(n-k)*A008289(n,k).
a(n) = A369596(n,n).
EXAMPLE
a(0) = 1: the empty permutation.
a(1) = 1: 1.
a(3) = 1: 213.
a(4) = 3: 1432, 2314, 3124.
a(5) = 13: 13542, 15243, 21435, 23415, 24135, 31425, 34125, 34215, 41235, 42351, 43125, 43215, 52314.
a(6) = 64: 123564, 123645, 132654, 134652, 136254, ..., 542136, 542316, 621435, 625413, 625431.
MAPLE
g:= proc(n) option remember; `if`(n=0, 1, n*g(n-1)+(-1)^n) end:
b:= proc(n, i, m) option remember; `if`(n>i*(i+1)/2, 0,
`if`(n=0, g(m), b(n, i-1, m)+b(n-i, min(n-i, i-1), m-1)))
end:
a:= n-> b(n$3):
seq(a(n), n=0..23);
CROSSREFS
Main diagonal of A369596.
Sequence in context: A065065 A020086 A151987 * A356485 A126149 A060927
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 02 2024
STATUS
approved