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A341232
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Numerator of the expected fraction of guests without a napkin in Conway's napkin problem with n guests.
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3
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0, 0, 1, 11, 39, 473, 19897, 63683, 5731597, 22926439, 280212089, 20175270749, 224810160067, 6294684482461, 1321883741325001, 1208579420640469, 68486167169628137, 17258514126746312369, 178860964586279976467, 6053755724458706915971, 3305350625554453976644453
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listen;
history;
text;
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OFFSET
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1,4
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REFERENCES
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Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A K Peters, 2004, p. 122.
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LINKS
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FORMULA
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a(n)/A341233(n) = Sum_{k=2..n} (1-2^(2-k))/k!.
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EXAMPLE
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0, 0, 1/12, 11/96, 39/320, 473/3840, 19897/161280, 63683/516096, 5731597/46448640
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PROG
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(Python)
from sympy import numer, S, factorial
return numer(sum((1-S(2)**(2-k))/factorial(k) for k in range(2, n+1)))
(Python)
from math import factorial
from fractions import Fraction
def a(n):
s = sum(Fraction(2**k-4, 2**k*factorial(k)) for k in range(2, n+1))
return s.numerator
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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