A285919 Number of ordered set partitions of [n] into four blocks such that equal-sized blocks are ordered with increasing least elements.

1, 40, 350, 3080, 17129, 82488, 464650, 1901680, 8357426, 35701952, 159721016, 627687060, 2642405289, 10712590392, 45568675202, 178738923440, 736145997686, 2946913512648, 12311241803256, 48275516469180, 197284995875314, 786939537437440, 3254422571085400

Offset: 4

Author

Alois P. Heinz, Apr 28 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..700
• Wikipedia, Partition of a set

Crossrefs

Column k=4 of A285824.

Cf. A285855.

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, 5)
    end:
a:= n-> coeff(b(n$2, 0), x, 4):
seq(a(n), n=4..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, 5}];
a[n_] := Coefficient[b[n, n, 0], x, 4];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)