A285919 Number of ordered set partitions of [n] into four blocks such that equal-sized blocks are ordered with increasing least elements.

1, 40, 350, 3080, 17129, 82488, 464650, 1901680, 8357426, 35701952, 159721016, 627687060, 2642405289, 10712590392, 45568675202, 178738923440, 736145997686, 2946913512648, 12311241803256, 48275516469180, 197284995875314, 786939537437440, 3254422571085400

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..700

Wikipedia, Partition of a set

Maple

b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
      (p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
      [multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 5)
    end:
a:= n-> coeff(b(n$2, 0), x, 4):
seq(a(n), n=4..30);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
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, 5}];
a[n_] := Coefficient[b[n, n, 0], x, 4];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)

Crossrefs

Column k=4 of A285824.

Cf. A285855.

Sequence in context: A365607 A247407 A251431 * A234913 A190312 A229532

Adjacent sequences: A285916 A285917 A285918 * A285920 A285921 A285922

Keyword

nonn

Author

Alois P. Heinz, Apr 28 2017

Status

approved