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

0,3

Links

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

Formula

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

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 *)

Crossrefs

Cf. A285824, A285862.

Sequence in context: A180821 A361889 A364369 * A197599 A197983 A351611

Adjacent sequences: A285923 A285924 A285925 * A285927 A285928 A285929

Keyword

nonn

Author

Alois P. Heinz, Apr 28 2017

Status

approved