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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124427 Sum of the sizes of the blocks containing the element 1 in all set partitions of {1,2,...,n}. 6
0, 1, 3, 9, 30, 112, 463, 2095, 10279, 54267, 306298, 1838320, 11677867, 78207601, 550277003, 4055549053, 31224520322, 250547144156, 2090779592827, 18110124715919, 162546260131455, 1509352980864191, 14478981877739094, 143299752100925452, 1461455003961745247 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..575

FORMULA

a(n) = Sum(k*binomial(n-1,k-1)*B(n-k), k=1..n) = Sum(k*A056857(n,k), k=1..n), where B(q) are the Bell numbers (A000110).

a(n) = (n-1)*B(n-1)+B(n). - Vladeta Jovovic, Nov 10 2006

EXAMPLE

a(3)=9 because the 5 (=A000110(3)) set partitions of {1,2,3} are 123, 12|3, 13|2, 1|23 and 1|2|3 and 3+2+2+1+1=9.

MAPLE

with(combinat): seq(add(k*binomial(n-1, k-1)*bell(n-k), k=1..n), n=0..30);

MATHEMATICA

Table[Sum[Binomial[n-1, k-1] * BellB[n-k] * k, {k, 1, n}], {n, 0, 22}] (* Geoffrey Critzer, Jun 14 2013 *)

Flatten[{0, Table[(n-1)*BellB[n-1] + BellB[n], {n, 1, 20}]}] (* Vaclav Kotesovec, Mar 19 2016, after Vladeta Jovovic *)

CROSSREFS

Cf. A000110, A056857.

Column p=1 of A270236 or of A270702.

Main diagonal of A270701.

Sequence in context: A107379 A117428 A134168 * A055730 A120018 A091353

Adjacent sequences:  A124424 A124425 A124426 * A124428 A124429 A124430

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Nov 10 2006

EXTENSIONS

a(0)=0 prepended by Alois P. Heinz, Mar 17 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 13 19:20 EST 2017. Contains 295976 sequences.