A285918 Number of ordered set partitions of [n] into three blocks such that equal-sized blocks are ordered with increasing least elements.

1, 18, 75, 420, 1218, 4242, 14563, 42930, 132528, 432960, 1250340, 3814629, 12073701, 35074482, 106044555, 331913202, 967193328, 2917846758, 9062084298, 26507831559, 79848170823, 246771097680, 723922691700, 2178960263415, 6709005218503, 19728686792637

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

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, 4)
    end:
a:= n-> coeff(b(n$2, 0), x, 3):
seq(a(n), n=3..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, 4}];
a[n_] := Coefficient[b[n, n, 0], x, 3];
Table[a[n], {n, 3, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)

Crossrefs

Column k=3 of A285824.

Cf. A285854.

Sequence in context: A284659 A143666 A139757 * A262402 A296363 A164603

Adjacent sequences: A285915 A285916 A285917 * A285919 A285920 A285921

Keyword

nonn

Author

Alois P. Heinz, Apr 28 2017

Status

approved