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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
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
a(n) ~ Bell(n) * (LambertW(n) + 1). - Vaclav Kotesovec, Jul 28 2021
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
Column p=1 of A270236 or of A270702.
Main diagonal of A270701.
Sequence in context: A117428 A339835 A134168 * A350589 A308554 A055730
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 10 2006
EXTENSIONS
a(0)=0 prepended by Alois P. Heinz, Mar 17 2016
STATUS
approved

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Last modified April 19 18:05 EDT 2024. Contains 371798 sequences. (Running on oeis4.)