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A192986 Numerator of Sum_{i=0..n-1} B(i)/B(n), where B(i) = A000110(i) are the Bell numbers. 2

%I

%S 0,1,1,4,3,6,76,279,289,5296,26443,71209,820988,5034585,16339511,

%T 223578344,1606536889,1007223253,94951548840,777028354999,

%U 1652442640014,58333928795428,533203744952179,2519959741699751,49191925338483848,495150794633289137,2566870563431644245

%N Numerator of Sum_{i=0..n-1} B(i)/B(n), where B(i) = A000110(i) are the Bell numbers.

%H G. C. Greubel, <a href="/A192986/b192986.txt">Table of n, a(n) for n = 0..500</a>

%H R. Kaye, <a href="http://dx.doi.org/10.1016/0020-0190(76)90014-4">A Gray code for set partitions</a>, Info. Proc. Letts., 5 (1976), 171-173.

%e 0, 1, 1, 4/5, 3/5, 6/13, 76/203, 279/877, 289/1035, 5296/21147, 26443/115975, ...

%t Table[Numerator[Sum[BellB[j], {j,0,n-1}]/BellB[n]], {n, 0, 30}] (* _G. C. Greubel_, Jul 25 2019 *)

%o (PARI) bell(n)=sum(k=0, n, stirling(n, k, 2));

%o vector(30, n, n--; numerator( sum(j=0, n-1, bell(j))/bell(n)) ) \\ _G. C. Greubel_, Jul 25 2019

%o (MAGMA) [0] cat [Numerator((&+[Bell(j): j in [0..n-1]])/Bell(n)): n in [1..30]]; // _G. C. Greubel_, Jul 25 2019

%o (Sage) [numerator(sum(bell_number(j) for j in (0..n-1))/bell_number(n)) for n in (0..30)] # _G. C. Greubel_, Jul 25 2019

%o (GAP) List([0..30], n-> NumeratorRat(Sum([0..n-1], j-> Bell(j))/Bell(n)) ); # _G. C. Greubel_, Jul 25 2019

%Y Cf. A000110, A192987.

%K nonn,frac

%O 0,4

%A _N. J. A. Sloane_, Jul 13 2011

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Last modified January 17 04:46 EST 2022. Contains 350378 sequences. (Running on oeis4.)