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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

%I

%S 0,1,3,9,30,112,463,2095,10279,54267,306298,1838320,11677867,78207601,

%T 550277003,4055549053,31224520322,250547144156,2090779592827,

%U 18110124715919,162546260131455,1509352980864191,14478981877739094,143299752100925452,1461455003961745247

%N Sum of the sizes of the blocks containing the element 1 in all set partitions of {1,2,...,n}.

%H Alois P. Heinz, <a href="/A124427/b124427.txt">Table of n, a(n) for n = 0..575</a>

%F 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).

%F a(n) = (n-1)*B(n-1)+B(n). - _Vladeta Jovovic_, Nov 10 2006

%e 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.

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

%t Table[Sum[Binomial[n-1,k-1] * BellB[n-k] * k, {k,1,n}], {n,0,22}] (* _Geoffrey Critzer_, Jun 14 2013 *)

%t Flatten[{0, Table[(n-1)*BellB[n-1] + BellB[n], {n, 1, 20}]}] (* _Vaclav Kotesovec_, Mar 19 2016, after _Vladeta Jovovic_ *)

%Y Cf. A000110, A056857.

%Y Column p=1 of A270236 or of A270702.

%Y Main diagonal of A270701.

%K nonn

%O 0,3

%A _Emeric Deutsch_, Nov 10 2006

%E a(0)=0 prepended by _Alois P. Heinz_, Mar 17 2016

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Last modified January 18 06:34 EST 2019. Contains 319269 sequences. (Running on oeis4.)