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A285920 Number of ordered set partitions of [n] into five blocks such that equal-sized blocks are ordered with increasing least elements.

%I A285920 #10 May 17 2018 08:10:40
%S A285920 1,75,1225,15750,152355,1049895,8130925,51541050,305751160,1721589870,
%T A285920 10370592050,54481859250,292852136335,1539187989915,8149972381105,
%U A285920 43456591157700,220640087499230,1133640238666320,5822084961637780,29811110400741780,154396823960132126
%N A285920 Number of ordered set partitions of [n] into five blocks such that equal-sized blocks are ordered with increasing least elements.
%H A285920 Alois P. Heinz, <a href="/A285920/b285920.txt">Table of n, a(n) for n = 5..700</a>
%H A285920 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A285920 b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
%p A285920       (p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
%p A285920       [multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 6)
%p A285920     end:
%p A285920 a:= n-> coeff(b(n$2, 0), x, 5):
%p A285920 seq(a(n), n=5..30);
%t A285920 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A285920 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, 6}];
%t A285920 a[n_] := Coefficient[b[n, n, 0], x, 5];
%t A285920 Table[a[n], {n, 5, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)
%Y A285920 Column k=5 of A285824.
%Y A285920 Cf. A285856.
%K A285920 nonn
%O A285920 5,2
%A A285920 _Alois P. Heinz_, Apr 28 2017