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

6,2

Links

Alois P. Heinz, Table of n, a(n) for n = 6..700

Wikipedia, Partition of a set

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 *)

Crossrefs

Column k=6 of A285824.

Cf. A285857.

Sequence in context: A202593 A293104 A267750 * A086024 A285857 A036403

Adjacent sequences: A285918 A285919 A285920 * A285922 A285923 A285924

Keyword

nonn

Author

Alois P. Heinz, Apr 28 2017

Status

approved