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A285925 Number of ordered set partitions of [n] into ten blocks such that equal-sized blocks are ordered with increasing least elements.

%I A285925 #11 May 17 2018 08:02:09
%S A285925 1,550,69025,4254250,201371170,7180042870,196518086050,4766802769300,
%T A285925 102889172957285,2006511403380770,36104901766271975,
%U A285925 597121503366547250,9381072363234242330,140940747710164417070,2033219852450765548790,28025263737301449789500
%N A285925 Number of ordered set partitions of [n] into ten blocks such that equal-sized blocks are ordered with increasing least elements.
%H A285925 Alois P. Heinz, <a href="/A285925/b285925.txt">Table of n, a(n) for n = 10..700</a>
%H A285925 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A285925 b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
%p A285925       (p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
%p A285925       [multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 11)
%p A285925     end:
%p A285925 a:= n-> coeff(b(n$2, 0), x, 10):
%p A285925 seq(a(n), n=10..30);
%t A285925 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A285925 b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[x^j*b[n - i*j, i - 1, p + j]*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2, {j, 0, n/i}]], {x, 0, 11}];
%t A285925 a[n_] := Coefficient[b[n, n, 0], x, 10];
%t A285925 Table[a[n], {n, 10, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)
%Y A285925 Column k=10 of A285824.
%Y A285925 Cf. A285861.
%K A285925 nonn
%O A285925 10,2
%A A285925 _Alois P. Heinz_, Apr 28 2017