A285921 - OEIS

%I #10 May 17 2018 08:10:50

%S 1,126,3486,63756,954387,9628542,97141022,886634892,7048863822,

%T 53483658228,397751490318,2858731936788,19510233553063,

%U 130084038669798,844004265958794,5657554841332464,35647504639822614,227439073802247384,1425548351910315534,8934412155886521480

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

%H Alois P. Heinz, <a href="/A285921/b285921.txt">Table of n, a(n) for n = 6..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, 7)

%p     end:

%p a:= n-> coeff(b(n$2, 0), x, 6):

%p seq(a(n), n=6..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, 7}];

%t a[n_] := Coefficient[b[n, n, 0], x, 6];

%t Table[a[n], {n, 6, 30}] (* _Jean-François Alcover_, May 17 2018, translated from Maple *)

%Y Column k=6 of A285824.

%Y Cf. A285857.

%K nonn

%O 6,2

%A _Alois P. Heinz_, Apr 28 2017