The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A262071

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A262071

Number T(n,k) of ordered partitions of an n-set with nondecreasing block sizes and maximal block size equal to k; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
(history; published version)

#20 by Alois P. Heinz at Fri Oct 26 18:43:27 EDT 2018

STATUS

editing

approved

#19 by Alois P. Heinz at Wed Oct 24 16:03:33 EDT 2018

EXAMPLE

1;

0, 1;

0, 2, 1;

0, 6, 3, 1;

0, 24, 18, 4, 1;

0, 120, 90, 30, 5, 1;

0, 720, 630, 200, 45, 6, 1;

0, 5040, 4410, 1610, 350, 63, 7, 1;

0, 40320, 37800, 13440, 3290, 560, 84, 8, 1;

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approved

editing

#18 by Bruno Berselli at Mon Dec 12 02:50:14 EST 2016

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reviewed

approved

#17 by Joerg Arndt at Mon Dec 12 02:43:40 EST 2016

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proposed

reviewed

#16 by Jean-François Alcover at Mon Dec 12 02:41:52 EST 2016

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editing

proposed

#15 by Jean-François Alcover at Mon Dec 12 02:41:46 EST 2016

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + If[i > n, 0, Binomial[n, i]*b[n - i, i]]]]; T[n_, k_] := b[n, k] - If[k == 0, 0, b[n, k - 1]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 12 2016, Alois P. Heinz *)

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approved

editing

#14 by Alois P. Heinz at Sun May 01 17:25:06 EDT 2016

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editing

approved

#13 by Alois P. Heinz at Sun May 01 17:25:01 EDT 2016

DATA

1, 0, 1, 0, 2, 1, 0, 6, 3, 1, 0, 24, 18, 4, 1, 0, 120, 90, 30, 5, 1, 0, 720, 630, 200, 45, 6, 1, 0, 5040, 4410, 1610, 350, 63, 7, 1, 0, 40320, 37800, 13440, 3290, 560, 84, 8, 1, 0, 362880, 340200, 130200, 30870, 5922, 840, 108, 9, 1, 0, 3628800, 3515400, 1327200, 334950, 61992, 9870, 1200, 135, 10, 1

#12 by Alois P. Heinz at Sun May 01 17:17:17 EDT 2016

CROSSREFS

Columns k=0-1 10 give: A000007, A000142 (for n>0), A272492, A272493, A272494, A272495, A272496, A272497, A272498, A272499, A272500.

STATUS

approved

editing

#11 by Alois P. Heinz at Wed Dec 30 20:04:06 EST 2015

STATUS

editing

approved