The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A056859

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A056859

Triangle of number of falls in set partitions of n.
(history; published version)

#20 by Alois P. Heinz at Tue May 24 03:06:34 EDT 2016

STATUS

proposed

approved

#19 by Jean-François Alcover at Tue May 24 00:20:07 EDT 2016

STATUS

editing

proposed

#18 by Jean-François Alcover at Tue May 24 00:20:00 EDT 2016

MATHEMATICA

b[n_, i_, m_] := b[n, i, m] = If[n == 0, x, Expand[Sum[b[n - 1, j, Max[m, j]]*If[j < i, x, 1], {j, 1, m + 1}]]];

T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 1, n}]][b[n, 1, 0]];

Table[T[n], {n, 1, 12}] // Flatten (* Jean-François Alcover, May 24 2016, after Alois P. Heinz *)

STATUS

approved

editing

#17 by Alois P. Heinz at Thu Mar 24 13:14:07 EDT 2016

STATUS

editing

approved

#16 by Alois P. Heinz at Thu Mar 24 13:14:02 EDT 2016

LINKS

Alois P. Heinz, <a href="/A056859/b056859.txt">Rows n = 1..100, flattened</a>

MAPLE

b:= proc(n, i, m) option remember;

`if`(n=0, x, expand(add(b(n-1, j, max(m, j))*

`if`(j<i, x, 1), j=1..m+1)))

end:

T:= n-> (p-> seq(coeff(p, x, i), i=1..n))(b(n, 1, 0)):

seq(T(n), n=1..12); # Alois P. Heinz, Mar 24 2016

#15 by Alois P. Heinz at Thu Mar 24 11:17:02 EDT 2016

DATA

1, 2, 0, 4, 1, 0, 8, 7, 0, 0, 16, 32, 4, 0, 0, 32, 121, 49, 1, 0, 0, 64, 411, 360, 42, 0, 0, 0, 128, 1304, 2062, 624, 22, 0, 0, 0, 256, 3949, 10163, 6042, 730, 7, 0, 0, 0, 512, 11567, 45298, 45810, 12170, 617, 1, 0, 0, 0, 1024, 33056, 187941, 296017, 141822, 18325, 385, 0, 0, 0, 0

STATUS

approved

editing

#14 by R. J. Mathar at Fri Mar 04 14:48:07 EST 2016

STATUS

editing

approved

#13 by R. J. Mathar at Fri Mar 04 14:47:48 EST 2016

EXAMPLE

32,121,49,1,0,0; ...

64,411,360,42,0,0,0;

128,1304,2062,624,22,0,0,0;

256,3949,10163,6042,730,7,0,0,0;

512,11567,45298,45810,12170,617,1,0,0,0;

1024,33056,187941,296017,141822,18325,385,0,0,0,0;

2048,92721,739352,1708893,1318395,330407,21605,176,0,0,0,0;

STATUS

approved

editing

#12 by R. J. Mathar at Fri Mar 04 14:32:42 EST 2016

STATUS

editing

approved

#11 by R. J. Mathar at Fri Mar 04 14:32:21 EST 2016

EXAMPLE

T(n=3,f=0)=4 counts the partitions {1,1,1}, {1,1,2}, {1,2,2}, and {1,2,3}. T(n=3,f=1) counts the partition {1,2,1}. - R. J. Mathar, Mar 04 2016