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A271764 Number of set partitions of [n] with minimal block length multiplicity equal to four. 2
1, 0, 0, 0, 105, 0, 0, 0, 67375, 135135, 1261260, 675675, 50925875, 97847750, 703993290, 6215737710, 228687298476, 58017429575, 11262925616250, 72813288304295, 2841531210935725, 11311740884766630, 252469888906590355, 2207276997956560530, 28579415631325499655 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..577

Wikipedia, Partition of a set

FORMULA

a(n) = A271424(n,4).

MAPLE

with(combinat):

b:= proc(n, i, k) option remember; `if`(n=0, 1,

      `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)

        *b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))

    end:

a:= n-> b(n$2, 4)-b(n$2, 5):

seq(a(n), n=4..30);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Join[{n - i*j}, Table[i, j]]]*b[n - i*j, i - 1, k]/j!, {j, Join[{0}, Range[k, n/i]]}]]];

a[n_] := b[n, n, 4] - b[n, n, 5];

Table[a[n], {n, 4, 30}] (* Jean-Fran├žois Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=4 of A271424.

Sequence in context: A091539 A157874 A282188 * A069172 A231578 A104437

Adjacent sequences:  A271761 A271762 A271763 * A271765 A271766 A271767

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 13 2016

STATUS

approved

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Last modified April 9 07:30 EDT 2020. Contains 333344 sequences. (Running on oeis4.)