A285924 Number of ordered set partitions of [n] into nine blocks such that equal-sized blocks are ordered with increasing least elements.

1, 405, 37125, 1738935, 64914993, 1775214441, 38186115825, 751359827790, 13076544824343, 207877406991111, 3041686131983343, 41512373437449915, 544051964769008601, 6850772610392201733, 82608610920666732693, 956263706215482795570, 10851693841665124551180

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..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, 10)
    end:
a:= n-> coeff(b(n$2, 0), x, 9):
seq(a(n), n=9..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, 10}];
a[n_] := Coefficient[b[n, n, 0], x, 9];
Table[a[n], {n, 9, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)

Crossrefs

Column k=9 of A285824.

Cf. A285860.

Sequence in context: A239541 A187134 A185839 * A285860 A151634 A368367

Adjacent sequences: A285921 A285922 A285923 * A285925 A285926 A285927

Keyword

nonn

Author

Alois P. Heinz, Apr 28 2017

Status

approved