cp's OEIS Frontend

A285924 Number of ordered set partitions of [n] into nine blocks such that equal-sized blocks are ordered with increasing least elements.

%I A285924 #10 May 17 2018 08:03:36
%S A285924 1,405,37125,1738935,64914993,1775214441,38186115825,751359827790,
%T A285924 13076544824343,207877406991111,3041686131983343,41512373437449915,
%U A285924 544051964769008601,6850772610392201733,82608610920666732693,956263706215482795570,10851693841665124551180
%N A285924 Number of ordered set partitions of [n] into nine blocks such that equal-sized blocks are ordered with increasing least elements.
%H A285924 Alois P. Heinz, <a href="/A285924/b285924.txt">Table of n, a(n) for n = 9..700</a>
%H A285924 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A285924 b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
%p A285924       (p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
%p A285924       [multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 10)
%p A285924     end:
%p A285924 a:= n-> coeff(b(n$2, 0), x, 9):
%p A285924 seq(a(n), n=9..30);
%t A285924 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A285924 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, 10}];
%t A285924 a[n_] := Coefficient[b[n, n, 0], x, 9];
%t A285924 Table[a[n], {n, 9, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)
%Y A285924 Column k=9 of A285824.
%Y A285924 Cf. A285860.
%K A285924 nonn
%O A285924 9,2
%A A285924 _Alois P. Heinz_, Apr 28 2017