A285923 Number of ordered set partitions of [n] into eight blocks such that equal-sized blocks are ordered with increasing least elements.

1, 288, 18600, 649440, 18650346, 378728064, 6346968056, 99768480240, 1370094506209, 17452476893280, 204026690329800, 2291047776886752, 24663963563727574, 256637317406331648, 2540192740448641960, 24558666993552144288, 233835181800425532162

Offset: 8

Author

Alois P. Heinz, Apr 28 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..700
• Wikipedia, Partition of a set

Crossrefs

Column k=8 of A285824.

Cf. A285859.

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, 9)
    end:
a:= n-> coeff(b(n$2, 0), x, 8):
seq(a(n), n=8..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, 9}];
a[n_] := Coefficient[b[n, n, 0], x, 8];
Table[a[n], {n, 8, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)