A285926 Number of ordered set partitions of [2n] into n blocks such that equal-sized blocks are ordered with increasing least elements.

1, 1, 11, 420, 17129, 1049895, 97141022, 10742461730, 1370094506209, 207877406991111, 36104901766271975, 7033373902938469086, 1531762189401458287506, 368890302956243012167470, 97283928918541409263666020, 27895730515878936009534815250

Offset: 0

Author

Alois P. Heinz, Apr 28 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..190

Crossrefs

Cf. A285824, A285862.

Programs

Maple

b:= proc(n, i, p) option remember; expand(`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)))
    end:
a:= n-> coeff(b(2*n$2, 0), x, n):
seq(a(n), n=0..20);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Expand[If[n == 0 || i == 1, (p + n)!/n! x^n, Sum[b[n - i j, i - 1, p + j] x^j multinomial[n, Join[{n - i j}, Table[i, j]]]/j!^2, {j, 0, n/i}]]];
a[n_] := Coefficient[b[2n, 2n, 0], x, n];
a /@ Range[0, 20] (* Jean-François Alcover, Dec 08 2020, after Alois P. Heinz *)

Formula

a(n) = A285824(2n,n).