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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); MATHEMATICA b[n_, i_, l_] := b[n, i, l] = If[n == 0, Product[j!, {j, l}], With[{m = Length[l]}, Sum[If[i == j || n*j == 1, 0, b[n-1, j, If[j>m, Append[l, 0], ReplacePart[l, j -> l[[j]]+1]]]], {j, 1, m+1}]]]; a[n_] := If[n == 1, 1, n! - b[n-1, 1, {0}]]; Array[a, 15] (* Jean-François Alcover, Mar 13 2021, after Alois P. Heinz *) CROSSREFS Column k=1 of A277031. Cf. A002467, A180191, A276975. Sequence in context: A137961 A334716 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 May 28 15:40 EDT 2023. Contains 363019 sequences. (Running on oeis4.)