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%I #10 May 17 2018 08:06:31
%S 1,196,8526,217560,4635939,67454772,877414538,10742461730,
%T 113528563148,1132899916148,10494458555126,96114856972680,
%U 831333224017303,7005224782844764,56197005110455286,453234116137501160,3555422918860518398,27541742188014185824
%N Number of ordered set partitions of [n] into seven blocks such that equal-sized blocks are ordered with increasing least elements.
%H Alois P. Heinz, <a href="/A285922/b285922.txt">Table of n, a(n) for n = 7..700</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
%p (p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
%p [multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 8)
%p end:
%p a:= n-> coeff(b(n$2, 0), x, 7):
%p seq(a(n), n=7..30);
%t multinomial[n_, k_List] := n!/Times @@ (k!);
%t 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, 8}] ;
%t a[n_] := Coefficient[b[n, n, 0], x, 7];
%t Table[a[n], {n, 7, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)
%Y Column k=7 of A285824.
%Y Cf. A285858.
%K nonn
%O 7,2
%A _Alois P. Heinz_, Apr 28 2017
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