A285924 - OEIS

%I #10 May 17 2018 08:03:36

%S 1,405,37125,1738935,64914993,1775214441,38186115825,751359827790,

%T 13076544824343,207877406991111,3041686131983343,41512373437449915,

%U 544051964769008601,6850772610392201733,82608610920666732693,956263706215482795570,10851693841665124551180

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

%H Alois P. Heinz, <a href="/A285924/b285924.txt">Table of n, a(n) for n = 9..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, 10)

%p     end:

%p a:= n-> coeff(b(n$2, 0), x, 9):

%p seq(a(n), n=9..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, 10}];

%t a[n_] := Coefficient[b[n, n, 0], x, 9];

%t Table[a[n], {n, 9, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)

%Y Column k=9 of A285824.

%Y Cf. A285860.

%K nonn

%O 9,2

%A _Alois P. Heinz_, Apr 28 2017