A285921 Number of ordered set partitions of [n] into six blocks such that equal-sized blocks are ordered with increasing least elements.

1, 126, 3486, 63756, 954387, 9628542, 97141022, 886634892, 7048863822, 53483658228, 397751490318, 2858731936788, 19510233553063, 130084038669798, 844004265958794, 5657554841332464, 35647504639822614, 227439073802247384, 1425548351910315534, 8934412155886521480

Offset: 6

Author

Alois P. Heinz, Apr 28 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..700
• Wikipedia, Partition of a set

Crossrefs

Column k=6 of A285824.

Cf. A285857.

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, 7)
    end:
a:= n-> coeff(b(n$2, 0), x, 6):
seq(a(n), n=6..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, 7}];
a[n_] := Coefficient[b[n, n, 0], x, 6];
Table[a[n], {n, 6, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)