A266518 Number of ordered partitions of a 2n-set with nondecreasing block sizes and maximal block size equal to n.

1, 2, 18, 200, 3290, 61992, 1480248, 39402792, 1229123610, 42349478600, 1640551617848, 69364811821032, 3222214209737432, 161656803984848200, 8772238289222220600, 509677254444910662000, 31677425399312755814970, 2092539622373193784503240

Offset: 0

Author

Alois P. Heinz, Dec 30 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A262071, A327801, A328156.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
       b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
    end:
a:= n-> `if`(n=0, 1, b(2*n, n)-b(2*n, n-1)):
seq(a(n), n=0..20);

Mathematica

b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, Binomial[n, i]*b[n-i, i]]]]; a[n_] := If[n==0, 1, b[2n, n] - b[2n, n-1]]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 27 2017, translated from Maple *)

Formula

a(n) = (2n)! * [x^n] Product_{i=1..n} (i-1)!/(i!-x^i).

a(n) = A262071(2n,n).

a(n) ~ c * 2^(2*n+1/2) * n^n / exp(n), where c = A247551 = 2.529477472079152648... . - Vaclav Kotesovec, Jan 02 2016

a(n) = A327801(2n,n). - Alois P. Heinz, Sep 26 2019