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A266518
Number of ordered partitions of a 2n-set with nondecreasing block sizes and maximal block size equal to n.
4
1, 2, 18, 200, 3290, 61992, 1480248, 39402792, 1229123610, 42349478600, 1640551617848, 69364811821032, 3222214209737432, 161656803984848200, 8772238289222220600, 509677254444910662000, 31677425399312755814970, 2092539622373193784503240
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 30 2015
STATUS
approved