A276923 Number of ordered set partitions of [2n] where the maximal block size equals n.

1, 2, 42, 860, 21490, 657972, 24011988, 1017804216, 49118959890, 2657929522820, 159340977018652, 10480673825750856, 750335572490293972, 58077997318270046600, 4832536579295065540200, 430136064463753547944560, 40779223639911413185024530

Offset: 0

Author

Alois P. Heinz, Sep 22 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..347

Crossrefs

Cf. A276922, A276961.

Programs

Maple

A:= proc(n, k) option remember; `if`(n=0, 1, add(
       A(n-i, k)*binomial(n, i), i=1..min(n, k)))
    end:
a:= n-> A(2*n, n) -`if`(n=0, 0, A(2*n, n-1)):
seq(a(n), n=0..20);

Mathematica

A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[A[n - i, k]*Binomial[n, i], {i, 1, Min[n, k]}]];
a[n_] := A[2*n, n] - If[n == 0, 0, A[2*n, n - 1]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jun 13 2018, translated from Maple *)

Formula

a(n) = A276922(2n,n).

a(n) ~ 2^(2*n-3/2) * n^(n+1) / (exp(n) * log(2)^(n+2)). - Vaclav Kotesovec, Sep 24 2016