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

Author

Alois P. Heinz, Apr 28 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..700
• Wikipedia, Partition of a set

Crossrefs

Column k=9 of A285824.

Cf. A285860.

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, 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 *)