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A277032 Number of permutations of [n] such that the minimal cyclic distance between elements of the same cycle equals one, a(1)=1 by convention. 2
1, 1, 5, 20, 109, 668, 4801, 38894, 353811, 3561512, 39374609, 474132730, 6179650125, 86676293916, 1301952953989, 20852719565694, 354771488612075, 6389625786835184, 121456993304945749, 2429966790591643402, 51042656559451380013, 1123165278137918510772 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..22.

Per Alexandersson et al., d-regular partitions and permutations, MathOverflow, 2014

EXAMPLE

a(2) = 1: (1,2).

a(3) = 5: (1,2,3), (1,3,2), (1)(2,3), (1,2)(3), (1,3)(2).

MAPLE

b:= proc(n, i, l) option remember; `if`(n=0, mul(j!, j=l),

      (m-> add(`if`(i=j or n*j=1, 0, b(n-1, j, `if`(j>m,

      [l[], 0], subsop(j=l[j]+1, l)))), j=1..m+1))(nops(l)))

    end:

a:= n-> `if`(n=1, 1, n!-b(n-1, 1, [0])):

seq(a(n), n=1..15);

CROSSREFS

Column k=1 of A277031.

Cf. A002467, A180191, A276975.

Sequence in context: A109500 A137961 A167145 * A300490 A020039 A319489

Adjacent sequences:  A277029 A277030 A277031 * A277033 A277034 A277035

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 25 2016

STATUS

approved

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Last modified November 12 22:16 EST 2019. Contains 329079 sequences. (Running on oeis4.)