The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A242027 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A242027

Number T(n,k) of endofunctions on [n] with cycles of k distinct lengths; triangle T(n,k), n>=0, 0<=k<=A003056(n), read by rows.
(history; published version)

#20 by Alois P. Heinz at Sat Feb 18 10:56:01 EST 2017

STATUS

proposed

approved

#19 by Jean-François Alcover at Sat Feb 18 10:37:19 EST 2017

STATUS

editing

proposed

#18 by Jean-François Alcover at Sat Feb 18 10:37:10 EST 2017

MATHEMATICA

multinomial[n_, k_] := n!/Times @@ (k!); b[n_, i_, k_] := b[n, i, k] = If[n == 0, If[k==0, 1, 0], If[i<1 || k<1, 0, Sum[(i-1)!^j*multinomial[n, Join[ {n-i*j}, Array[i&, j]]]/j!*b[n-i*j, i-1, k-If[j==0, 0, 1]], {j, 0, n/i}]] ]; T[0, 0] = 1; T[n_, k_] := Sum[Binomial[n-1, j-1]*n^(n-j)*b[j, j, k], {j, 0, n}]; Table[T[n, k], {n, 0, 14}, {k, 0, Floor[(Sqrt[1+8n]-1)/2]}] // Flatten (* Jean-François Alcover, Feb 18 2017, translated from Maple *)

STATUS

approved

editing

#17 by Alois P. Heinz at Thu Aug 21 18:06:03 EDT 2014

STATUS

editing

approved

#16 by Alois P. Heinz at Thu Aug 21 17:04:42 EDT 2014

CROSSREFS

Cf. A003056, A060281, A218868 (the same for permutations).

STATUS

approved

editing

#15 by Alois P. Heinz at Thu Aug 21 11:36:46 EDT 2014

STATUS

editing

approved

#14 by Alois P. Heinz at Thu Aug 21 10:00:56 EDT 2014

CROSSREFS

T(A000217(n*(),n+1)/2) gives A246292.

#13 by Alois P. Heinz at Thu Aug 21 09:59:49 EDT 2014

CROSSREFS

Columns k=0-1 10 give: A000007, A241980 for n>0, A246283, A246284, A246285, A246286, A246287, A246288, A246289, A246290, A246291.

T(n*(n+1)/2) gives A246292.

#12 by Alois P. Heinz at Thu Aug 21 09:21:52 EDT 2014

NAME

Number T(n,k) of endofunctions on [n] with cycles of k different distinct lengths; triangle T(n,k), n>=0, 0<=k<=A003056(n), read by rows.

STATUS

approved

editing

#11 by Alois P. Heinz at Mon Aug 11 15:15:44 EDT 2014

STATUS

editing

approved