login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A271762 Number of set partitions of [n] with minimal block length multiplicity equal to two. 2
1, 0, 3, 0, 55, 105, 945, 1218, 15456, 26785, 705573, 2502786, 32988670, 169561483, 1757881723, 10231748010, 84389906941, 540218433147, 6899156019034, 41756989590256, 554960234199955, 4793361957432730, 59690079139252499, 558283841454550850, 7093218105977514525 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..576

Wikipedia, Partition of a set

FORMULA

a(n) = A271424(n,2).

EXAMPLE

a(4) = 3: 12|34, 13|24, 14|23.

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, 2)-b(n$2, 3):

seq(a(n), n=2..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, 2] - b[n, n, 3];

Table[a[n], {n, 2, 30}] (* Jean-Fran├žois Alcover, May 15 2018, after Alois P. Heinz *)

CROSSREFS

Column k=2 of A271424.

Sequence in context: A009786 A012738 A193410 * A264882 A012759 A296621

Adjacent sequences:  A271759 A271760 A271761 * A271763 A271764 A271765

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 13 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 01:20 EST 2018. Contains 318141 sequences. (Running on oeis4.)