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A285921 Number of ordered set partitions of [n] into six blocks such that equal-sized blocks are ordered with increasing least elements. 3
1, 126, 3486, 63756, 954387, 9628542, 97141022, 886634892, 7048863822, 53483658228, 397751490318, 2858731936788, 19510233553063, 130084038669798, 844004265958794, 5657554841332464, 35647504639822614, 227439073802247384, 1425548351910315534, 8934412155886521480 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..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, 7)

    end:

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

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

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

Table[a[n], {n, 6, 30}] (* Jean-Fran├žois Alcover, May 17 2018, translated from Maple *)

CROSSREFS

Column k=6 of A285824.

Cf. A285857.

Sequence in context: A202593 A293104 A267750 * A086024 A285857 A036403

Adjacent sequences:  A285918 A285919 A285920 * A285922 A285923 A285924

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 28 2017

STATUS

approved

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Last modified June 6 01:16 EDT 2020. Contains 334858 sequences. (Running on oeis4.)