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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.

%I A285926 #9 Dec 08 2020 08:36:08
%S A285926 1,1,11,420,17129,1049895,97141022,10742461730,1370094506209,
%T A285926 207877406991111,36104901766271975,7033373902938469086,
%U A285926 1531762189401458287506,368890302956243012167470,97283928918541409263666020,27895730515878936009534815250
%N A285926 Number of ordered set partitions of [2n] into n blocks such that equal-sized blocks are ordered with increasing least elements.
%H A285926 Alois P. Heinz, <a href="/A285926/b285926.txt">Table of n, a(n) for n = 0..190</a>
%F A285926 a(n) = A285824(2n,n).
%p A285926 b:= proc(n, i, p) option remember; expand(`if`(n=0 or i=1,
%p A285926       (p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
%p A285926       [multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)))
%p A285926     end:
%p A285926 a:= n-> coeff(b(2*n$2, 0), x, n):
%p A285926 seq(a(n), n=0..20);
%t A285926 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A285926 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}]]];
%t A285926 a[n_] := Coefficient[b[2n, 2n, 0], x, n];
%t A285926 a /@ Range[0, 20] (* _Jean-François Alcover_, Dec 08 2020, after _Alois P. Heinz_ *)
%Y A285926 Cf. A285824, A285862.
%K A285926 nonn
%O A285926 0,3
%A A285926 _Alois P. Heinz_, Apr 28 2017