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A271426 Number of set partitions of [n] with minimal block length multiplicity equal to one. 2
0, 1, 1, 4, 11, 51, 132, 771, 3089, 18388, 96423, 627529, 3349018, 24510305, 155908651, 1171494200, 8647906143, 71603237483, 572103586280, 5172888505403, 43344865682187, 416735802793600, 3830340992280773, 38239507035358011, 374336654847685014 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

At least one block length occurs exactly once.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..576

Wikipedia, Partition of a set

FORMULA

a(n) = A271424(n,1).

EXAMPLE

a(1) = 1: 1.

a(2) = 1: 12.

a(3) = 4: 123, 12|3, 13|2, 1|23.

a(4) = 11: 1234, 123|4, 124|3, 12|3|4, 134|2, 13|2|4, 1|234, 1|23|4, 14|2|3, 1|24|3, 1|2|34.

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, 1)-b(n$2, 2):

seq(a(n), n=0..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, 1] - b[n, n, 2];

Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 07 2018, after Alois P. Heinz *)

CROSSREFS

Column k=1 of A271424.

Sequence in context: A149314 A149315 A149316 * A218957 A149317 A027042

Adjacent sequences:  A271423 A271424 A271425 * A271427 A271428 A271429

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 07 2016

STATUS

approved

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Last modified May 27 15:41 EDT 2018. Contains 304696 sequences. (Running on oeis4.)