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A285926 Number of ordered set partitions of [2n] into n blocks such that equal-sized blocks are ordered with increasing least elements. 3
1, 1, 11, 420, 17129, 1049895, 97141022, 10742461730, 1370094506209, 207877406991111, 36104901766271975, 7033373902938469086, 1531762189401458287506, 368890302956243012167470, 97283928918541409263666020, 27895730515878936009534815250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..190

FORMULA

a(n) = A285824(2n,n).

MAPLE

b:= proc(n, i, p) option remember; expand(`if`(n=0 or i=1,

(p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat

[multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)))

end:

a:= n-> coeff(b(2*n$2, 0), x, n):

seq(a(n), n=0..20);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_, p_] := b[n, i, p] = Expand[If[n == 0 || i == 1, (p + n)!/n! x^n, Sum[b[n - i j, i - 1, p + j] x^j multinomial[n, Join[{n - i j}, Table[i, j]]]/j!^2, {j, 0, n/i}]]];

a[n_] := Coefficient[b[2n, 2n, 0], x, n];

a /@ Range[0, 20] (* Jean-François Alcover, Dec 08 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A285824, A285862.

Sequence in context: A046281 A180833 A180821 * A197599 A197983 A351611

Adjacent sequences: A285923 A285924 A285925 * A285927 A285928 A285929

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 28 2017

STATUS

approved

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Last modified December 9 18:21 EST 2022. Contains 358703 sequences. (Running on oeis4.)