The On-Line Encyclopedia of Integer Sequences (OEIS)

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A285922

Number of ordered set partitions of [n] into seven blocks such that equal-sized blocks are ordered with increasing least elements.
(history; published version)

#10 by Alois P. Heinz at Thu May 17 08:06:31 EDT 2018

STATUS

proposed

approved

#9 by Jean-François Alcover at Thu May 17 07:53:22 EDT 2018

STATUS

editing

proposed

#8 by Jean-François Alcover at Thu May 17 07:53:17 EDT 2018

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[x^j*b[n - i*j, i - 1, p + j]*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2, {j, 0, n/i}]], {x, 0, 8}] ;

a[n_] := Coefficient[b[n, n, 0], x, 7];

Table[a[n], {n, 7, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)

STATUS

approved

editing

#7 by Alois P. Heinz at Sat Apr 29 19:05:06 EDT 2017

STATUS

editing

approved

#6 by Alois P. Heinz at Sat Apr 29 19:05:02 EDT 2017

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

STATUS

approved

editing

#5 by Alois P. Heinz at Sat Apr 29 18:19:50 EDT 2017

STATUS

editing

approved

#4 by Alois P. Heinz at Sat Apr 29 18:19:46 EDT 2017

LINKS

Alois P. Heinz, <a href="/A285922/b285922.txt">Table of n, a(n) for n = 7..700</a>

#3 by Alois P. Heinz at Sat Apr 29 15:44:33 EDT 2017

MAPLE

b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,

(p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat

[multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 8)

end:

a:= n-> coeff(b(n$2, 0), x, 7):

seq(a(n), n=7..30);

CROSSREFS

Cf. A285858.

#2 by Alois P. Heinz at Fri Apr 28 17:10:11 EDT 2017

NAME

allocated for Alois P. Heinz

Number of ordered set partitions of [n] into seven blocks such that equal-sized blocks are ordered with increasing least elements.

DATA

1, 196, 8526, 217560, 4635939, 67454772, 877414538, 10742461730, 113528563148, 1132899916148, 10494458555126, 96114856972680, 831333224017303, 7005224782844764, 56197005110455286, 453234116137501160, 3555422918860518398, 27541742188014185824

OFFSET

7,2

CROSSREFS

Column k=7 of A285824.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Apr 28 2017

STATUS

approved

editing

#1 by Alois P. Heinz at Fri Apr 28 16:55:07 EDT 2017

NAME

allocated for Alois P. Heinz

KEYWORD

allocated

STATUS

approved