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A285920 Number of ordered set partitions of [n] into five blocks such that equal-sized blocks are ordered with increasing least elements. 3
1, 75, 1225, 15750, 152355, 1049895, 8130925, 51541050, 305751160, 1721589870, 10370592050, 54481859250, 292852136335, 1539187989915, 8149972381105, 43456591157700, 220640087499230, 1133640238666320, 5822084961637780, 29811110400741780, 154396823960132126 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..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, 6)

    end:

a:= n-> coeff(b(n$2, 0), x, 5):

seq(a(n), n=5..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, 6}];

a[n_] := Coefficient[b[n, n, 0], x, 5];

Table[a[n], {n, 5, 30}] (* Jean-Fran├žois Alcover, May 17 2018, translated from Maple *)

CROSSREFS

Column k=5 of A285824.

Cf. A285856.

Sequence in context: A264673 A320618 A218094 * A293581 A210047 A210505

Adjacent sequences:  A285917 A285918 A285919 * A285921 A285922 A285923

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 28 2017

STATUS

approved

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Last modified October 6 04:36 EDT 2022. Contains 357261 sequences. (Running on oeis4.)