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URL: https://oeis.org/A192987

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A192987
Denominator of Sum_{i=0..n-1} B(i)/B(n), where B(i) = A000110(i) are the Bell numbers.
2
1, 1, 1, 5, 5, 13, 203, 877, 1035, 21147, 115975, 339285, 4213597, 27644437, 95449661, 1382958545, 10480142147, 6905405817, 682076806159, 5832742205057, 12931039558843, 474869816156751, 4506715738447323, 22076002927542173, 445958869294805289, 4638590332229999353
OFFSET
0,4
LINKS
R. Kaye, A Gray code for set partitions, Info. Proc. Letts., 5 (1976), 171-173.
FORMULA
A192986(n)/a(n) ~ LambertW(n)/n. - Vaclav Kotesovec, Jun 29 2025
EXAMPLE
0, 1, 1, 4/5, 3/5, 6/13, 76/203, 279/877, 289/1035, 5296/21147, 26443/115975, ...
MATHEMATICA
Table[Denominator[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--; denominator( sum(j=0, n-1, bell(j))/bell(n)) ) \\ G. C. Greubel, Jul 25 2019
(Magma) [1] cat [Denominator((&+[Bell(j): j in [0..n-1]])/Bell(n)): n in [1..30]]; // G. C. Greubel, Jul 25 2019
(SageMath) [denominator(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-> DenominatorRat(Sum([0..n-1], j-> Bell(j))/Bell(n) )); # G. C. Greubel, Jul 25 2019
CROSSREFS
Sequence in context: A126439 A318541 A076903 * A252768 A062367 A286257
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Jul 13 2011
STATUS
approved