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A246073 Number of permutations p on [2n] satisfying p^n(i) = i for all i in [n]. 2
1, 1, 10, 108, 6672, 109200, 45007920, 983324160, 665546434560, 60174422501760, 32648180513760000, 4656975300322329600, 13859947861644771532800, 1193599114668580293273600, 1257285172911535450293811200, 766119340152013216053484800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjecture: Lim inf n->infinity a(n) / (((n-1)!)^2 * 4^(n-1) / sqrt(n)) = 1.128... . - Vaclav Kotesovec, Aug 14 2014

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..233 (first 100 terms from Alois P. Heinz)

Vaclav Kotesovec, Graph - asymptotic

FORMULA

a(n) = A246072(2n,n).

EXAMPLE

a(2) = 10: (1,2,3,4), (1,2,4,3), (1,3,2,4), (1,4,3,2), (2,1,3,4), (2,1,4,3), (3,2,1,4), (3,4,1,2), (4,2,3,1), (4,3,2,1).

a(3) = 108: (1,2,3,4,5,6), (1,2,3,4,6,5), (1,2,3,5,4,6), ... (6,4,2,3,1,5), (6,5,1,2,4,3), (6,5,2,1,3,4).

MAPLE

with(numtheory): with(combinat): M:=multinomial:

b:= proc(n, k, p) local l, g; l, g:= sort([divisors(p)[]]),

      proc(k, m, i, t) option remember; local d, j; d:= l[i];

        `if`(i=1, m!, add(M(k, k-(d-t)*j, (d-t)$j)/j!*

         (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,

        `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),

        `if`(t=0, [][], m/t))))

      end; g(k, n-k, nops(l), 0)

    end:

a:= n-> `if`(n=0, 1, b(2*n, n, n)):

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

CROSSREFS

Main diagonal of A246072.

Sequence in context: A059524 A190957 A163206 * A261920 A024527 A291894

Adjacent sequences:  A246070 A246071 A246072 * A246074 A246075 A246076

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 12 2014

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)