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A285921 Number of ordered set partitions of [n] into six blocks such that equal-sized blocks are ordered with increasing least elements.

%I A285921 #10 May 17 2018 08:10:50
%S A285921 1,126,3486,63756,954387,9628542,97141022,886634892,7048863822,
%T A285921 53483658228,397751490318,2858731936788,19510233553063,
%U A285921 130084038669798,844004265958794,5657554841332464,35647504639822614,227439073802247384,1425548351910315534,8934412155886521480
%N A285921 Number of ordered set partitions of [n] into six blocks such that equal-sized blocks are ordered with increasing least elements.
%H A285921 Alois P. Heinz, <a href="/A285921/b285921.txt">Table of n, a(n) for n = 6..700</a>
%H A285921 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A285921 b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
%p A285921       (p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
%p A285921       [multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 7)
%p A285921     end:
%p A285921 a:= n-> coeff(b(n$2, 0), x, 6):
%p A285921 seq(a(n), n=6..30);
%t A285921 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A285921 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, 7}];
%t A285921 a[n_] := Coefficient[b[n, n, 0], x, 6];
%t A285921 Table[a[n], {n, 6, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)
%Y A285921 Column k=6 of A285824.
%Y A285921 Cf. A285857.
%K A285921 nonn
%O A285921 6,2
%A A285921 _Alois P. Heinz_, Apr 28 2017