The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A256554

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A256554

Number T(n,k) of cycle types of degree-n permutations having the k-th smallest possible order; triangle T(n,k), n>=0, 1<=k<=A009490(n), read by rows.
(history; published version)

#31 by Alois P. Heinz at Wed May 09 09:56:57 EDT 2018

STATUS

editing

approved

#30 by Alois P. Heinz at Wed May 09 09:56:54 EDT 2018

EXAMPLE

Triangle T(n,k) begins:

1;

1, 1;

1, 1, 1;

1, 2, 1, 1;

1, 2, 1, 1, 1, 1;

1, 3, 2, 2, 1, 2;

1, 3, 2, 2, 1, 3, 1, 1, 1;

1, 4, 2, 4, 1, 5, 1, 1, 1, 1, 1;

1, 4, 3, 4, 1, 7, 1, 1, 1, 2, 2, 1, 1, 1;

1, 5, 3, 6, 2, 9, 1, 2, 1, 3, 4, 1, 1, 1, 1, 1;

STATUS

approved

editing

#29 by Bruno Berselli at Mon Jan 23 09:21:08 EST 2017

STATUS

proposed

approved

#28 by Jean-François Alcover at Mon Jan 23 09:00:58 EST 2017

STATUS

editing

proposed

#27 by Jean-François Alcover at Mon Jan 23 09:00:54 EST 2017

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0 || i == 1, x, b[n, i - 1] + Function[p, Sum[Coefficient[p, x, t]*x^LCM[t, i], {t, 1, Exponent[p, x]}]][Sum[b[n - i*j, i - 1], {j, 1, n/i}]]]; T[n_] := Function[p, Table[Function[h, If[h == 0, {{}, {}}, h]][Coefficient[p, x, i]], {i, 1, Exponent[p, x]}]][b[n, n]]; Table[T[n], {n, 0, 12}] // Flatten (* Jean-François Alcover, Jan 23 2017, translated from Maple *)

STATUS

approved

editing

#26 by Alois P. Heinz at Mon Aug 31 20:38:53 EDT 2015

STATUS

editing

approved

#25 by Alois P. Heinz at Mon Aug 31 20:38:49 EDT 2015

KEYWORD

nonn,look,tabf

STATUS

approved

editing

#24 by Alois P. Heinz at Sun May 31 03:27:27 EDT 2015

STATUS

editing

approved

#23 by Alois P. Heinz at Sun May 31 02:45:24 EDT 2015

CROSSREFS

Columns k=1-8 9 give: A000012, A004526, A002264, A008642(n-4), A002266, A074752, A132270, A008643(n-8) for n>7, A008649(n-9) for n>8.

#22 by Alois P. Heinz at Sun May 31 02:41:51 EDT 2015

CROSSREFS

Columns k=1-7 8 give: A000012, A004526, A002264, A008642(n-4), A002266, A074752, A132270, A008643(n-8) for n>7.