A285922 Number of ordered set partitions of [n] into seven blocks such that equal-sized blocks are ordered with increasing least elements.

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

Offset: 7

Author

Alois P. Heinz, Apr 28 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..700
• Wikipedia, Partition of a set

Crossrefs

Column k=7 of A285824.

Cf. A285858.

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, 8)
    end:
a:= n-> coeff(b(n$2, 0), x, 7):
seq(a(n), n=7..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, 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 *)