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A046825
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Numerator of Sum_{k=0..n} 1/C(n,k).
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18
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1, 2, 5, 8, 8, 13, 151, 256, 83, 146, 1433, 2588, 15341, 28211, 52235, 19456, 19345, 36362, 651745, 6168632, 1463914, 2786599, 122289917, 233836352, 140001721, 268709146, 774885169, 1491969394, 41711914513, 80530073893
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 294, Problem 7.15.
R. L. Graham, D. E. Knuth, O. Patashnik; Concrete Mathematics, Addison-Wesley, Reading (1994) 2nd Ed. Exercise 6.100.
G. Letac; Problemes de probabilites, Presses Universitaires de France (1970), p. 14
F. Nedemeyer and Y. Smorodinsky, Resistances in the multidimensional cube, Quantum 7:1 (1996) 12-15 and 63.
D. Singmaster, SIAM Review, 22 (1980) 504, Problem 79-16, Resistances in an n-Dimensional Cube.
B. Sury, Sum of the reciprocals of the binomial coefficients, Europ. J. Combinatorics, 14 (1993), 351-353.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
T. Mansour, Gamma function, beta function and combinatorial identities.
T. Sillke, More information
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FORMULA
| Let P(n) = 1/n Sum[ 1/binomial[ n-1, k ], {k, 0, n-1} ] = A046878(n)/A046879(n) = A046825(n-1)/(n*A046826(n-1)): { 0 1 1 5/6 2/3 8/15 ...}.
Then P(n) = 2^(-n) Sum[ 2^k / k, {k, 1, n} ] = 2^(-n+1) Sum[ binomial[ n, k ] / k, {k odd} ]; P(0) = 0, P(n) = P(n-1)/2 + 1/n - Torsten Sillke.
G.f. for P(n): (2*Log[ 1 - z ])/(-2 + z) - wouter.meeussen(AT)pandora.be.
P(n)=2^(-n)Sum[(binomial(n,k)+1)/k,k=1..n)
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EXAMPLE
| 1, 2, 5/2, 8/3, 8/3, 13/5, 151/60, 256/105, 83/35, 146/63, 1433/630, 2588/1155, 15341/6930, 28211/12870, 52235/24024, 19456/9009, 19345/9009, ... = A046825/A046826
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MATHEMATICA
| Numerator/@Table[Sum[1/Binomial[n, k], {k, 0, n}], {n, 0, 40}] (* From Harvey P. Dale, Apr 21 2011 *)
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CROSSREFS
| Cf. A003149, A046826, A048211, A051389, A100512, A100513.
Sequence in context: A103311 A019824 A019772 * A131716 A011279 A185094
Adjacent sequences: A046822 A046823 A046824 * A046826 A046827 A046828
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KEYWORD
| nonn,easy,frac,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Formulae, references and web page from Torsten.Sillke(AT)uni-bielefeld.de
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