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

0, 1, 1, 4, 3, 6, 76, 279, 289, 5296, 26443, 71209, 820988, 5034585, 16339511, 223578344, 1606536889, 1007223253, 94951548840, 777028354999, 1652442640014, 58333928795428, 533203744952179, 2519959741699751, 49191925338483848, 495150794633289137, 2566870563431644245

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

R. Kaye, A Gray code for set partitions, Info. Proc. Letts., 5 (1976), 171-173.

Example

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

Mathematica

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

Prog

(PARI) bell(n)=sum(k=0, n, stirling(n, k, 2));
vector(30, n, n--; numerator( sum(j=0, n-1, bell(j))/bell(n)) ) \\ G. C. Greubel, Jul 25 2019
(Magma) [0] cat [Numerator((&+[Bell(j): j in [0..n-1]])/Bell(n)): n in [1..30]]; // G. C. Greubel, Jul 25 2019
(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
(GAP) List([0..30], n-> NumeratorRat(Sum([0..n-1], j-> Bell(j))/Bell(n)) ); # G. C. Greubel, Jul 25 2019

Crossrefs

Cf. A000110, A192987.

Sequence in context: A276229 A077955 A077978 * A336741 A072816 A340012

Adjacent sequences: A192983 A192984 A192985 * A192987 A192988 A192989

Keyword

nonn,frac

Author

N. J. A. Sloane, Jul 13 2011

Status

approved