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

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..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, 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 *)

Crossrefs

Column k=7 of A285824.

Cf. A285858.

Sequence in context: A128990 A061619 A185900 * A285858 A203540 A006362

Adjacent sequences: A285919 A285920 A285921 * A285923 A285924 A285925

Keyword

nonn

Author

Alois P. Heinz, Apr 28 2017

Status

approved