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

0,2

Links

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

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

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 *)

Crossrefs

Cf. A276922, A276961.

Sequence in context: A318247 A038396 A287328 * A308526 A162678 A265867

Adjacent sequences: A276920 A276921 A276922 * A276924 A276925 A276926

Keyword

nonn

Author

Alois P. Heinz, Sep 22 2016

Status

approved