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A281262 Number of permutations of [2n] with exactly n fixed points. 3
1, 0, 6, 40, 630, 11088, 244860, 6362928, 190900710, 6490575520, 246642054516, 10358965584240, 476512419579196, 23825620968559200, 1286583532342313400, 74621844875699059680, 4626554382293942780550, 305352589231397889910080, 21374681246197861368840900 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..366

FORMULA

a(n) = (4*n-2)*((n-1)*a(n-1)+(4*n-6)*a(n-2))/n for n>1, a(n) = 1-n for n<2.

a(n) = binomial(2n,n) * A000166(n).

a(n) = A008290(2n,n) = A098825(2n,n).

EXAMPLE

a(2) = 6: 1243, 1324, 1432, 2134, 3214, 4231.

MAPLE

a:= proc(n) option remember; `if`(n<2, 1-n,

      (4*n-2)*((n-1)*a(n-1)+(4*n-6)*a(n-2))/n)

    end:

seq(a(n), n=0..20);

CROSSREFS

Cf. A000166, A007318, A008290, A098825.

Sequence in context: A053677 A204563 A196449 * A186196 A196478 A001367

Adjacent sequences:  A281259 A281260 A281261 * A281263 A281264 A281265

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 12 2017

STATUS

approved

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Last modified February 20 06:26 EST 2019. Contains 320332 sequences. (Running on oeis4.)