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

0,2

Links

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

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

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 *)

Crossrefs

Cf. A262071, A327801, A328156.

Sequence in context: A210989 A361877 A116072 * A303381 A224881 A369921

Adjacent sequences: A266515 A266516 A266517 * A266519 A266520 A266521

Keyword

nonn

Author

Alois P. Heinz, Dec 30 2015

Status

approved