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

Author

Alois P. Heinz, Apr 28 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..700
• Wikipedia, Partition of a set

Crossrefs

Column k=10 of A285824.

Cf. A285861.

Programs

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 *)