A285925 Number of ordered set partitions of [n] into ten blocks such that equal-sized blocks are ordered with increasing least elements.

1, 550, 69025, 4254250, 201371170, 7180042870, 196518086050, 4766802769300, 102889172957285, 2006511403380770, 36104901766271975, 597121503366547250, 9381072363234242330, 140940747710164417070, 2033219852450765548790, 28025263737301449789500

Offset

10,2

Links

Alois P. Heinz, Table of n, a(n) for n = 10..700

Wikipedia, Partition of a set

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, 11)
    end:
a:= n-> coeff(b(n$2, 0), x, 10):
seq(a(n), n=10..30);

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, 11}];
a[n_] := Coefficient[b[n, n, 0], x, 10];
Table[a[n], {n, 10, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)

Crossrefs

Column k=10 of A285824.

Cf. A285861.

Sequence in context: A189502 A190075 A234415 * A285861 A034282 A127347

Adjacent sequences: A285922 A285923 A285924 * A285926 A285927 A285928

Keyword

nonn

Author

Alois P. Heinz, Apr 28 2017

Status

approved