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A341233
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Denominator 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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1, 1, 12, 96, 320, 3840, 161280, 516096, 46448640, 185794560, 2270822400, 163499212800, 1821848371200, 51011754393600, 10712468422656000, 9794256843571200, 555007887802368000, 139861987726196736000, 1449478781889675264000, 49059281848573624320000
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OFFSET
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1,3
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LINKS
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FORMULA
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A341232(n)/a(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 denom, S, factorial
return denom(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.denominator
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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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