The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A256130 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A256130

Number T(n,k) of partitions of n into parts of exactly k sorts which are introduced in ascending order; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
(history; published version)

#28 by Alois P. Heinz at Wed Feb 14 16:52:09 EST 2024

STATUS

editing

approved

#27 by Alois P. Heinz at Wed Feb 14 16:52:07 EST 2024

EXAMPLE

...

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approved

editing

#26 by Alois P. Heinz at Fri Sep 28 05:42:53 EDT 2018

STATUS

editing

approved

#25 by Alois P. Heinz at Fri Sep 28 05:28:55 EDT 2018

CROSSREFS

Cf. A000142, A246935, A255970, A262495, A319730.

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approved

editing

#24 by Alois P. Heinz at Fri Sep 28 05:26:59 EDT 2018

STATUS

editing

approved

#23 by Alois P. Heinz at Tue Sep 25 18:31:28 EDT 2018

EXAMPLE

1;

0, 1;

0, 2, 1;

0, 3, 4, 1;

0, 5, 12, 7, 1;

0, 7, 30, 33, 11, 1;

0, 11, 72, 130, 77, 16, 1;

0, 15, 160, 463, 438, 157, 22, 1;

0, 22, 351, 1557, 2216, 1223, 289, 29, 1;

0, 30, 743, 5031, 10422, 8331, 2957, 492, 37, 1;

0, 42, 1561, 15877, 46731, 52078, 26073, 6401, 788, 46, 1;

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approved

editing

#22 by Michel Marcus at Sun Feb 21 12:03:16 EST 2016

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reviewed

approved

#21 by Joerg Arndt at Sun Feb 21 11:31:50 EST 2016

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proposed

reviewed

#20 by Jean-François Alcover at Sun Feb 21 10:16:49 EST 2016

STATUS

editing

proposed

#19 by Jean-François Alcover at Sun Feb 21 10:16:43 EST 2016

MATHEMATICA

b[n_, i_, k_] := b[n, i, k] = If[n==0, 1, If[i<1, 0, b[n, i-1, k] + If[i>n, 0, k*b[n-i, i, k]]]]; T[n_, k_] := Sum[b[n, n, k-i]*(-1)^i/(i!*(k-i)!), {i, 0, k}]; Table[Table[T[n, k], {k, 0, n}], {n, 0, 10}] // Flatten (* Jean-François Alcover, Feb 21 2016, after Alois P. Heinz *)

STATUS

approved

editing