A341233 - OEIS

%I #15 Feb 08 2021 11:47:10

%S 1,1,12,96,320,3840,161280,516096,46448640,185794560,2270822400,

%T 163499212800,1821848371200,51011754393600,10712468422656000,

%U 9794256843571200,555007887802368000,139861987726196736000,1449478781889675264000,49059281848573624320000

%N Denominator of the expected fraction of guests without a napkin in Conway's napkin problem with n guests.

%F A341232(n)/a(n) = Sum_{k=2..n} (1-2^(2-k))/k!.

%F Lim_{n->oo} A341232(n)/a(n) = (2-sqrt(e))^2 (A248788).

%e 0, 0, 1/12, 11/96, 39/320, 473/3840, 19897/161280, 63683/516096, 5731597/46448640

%o (Python)

%o from sympy import denom, S, factorial

%o def A341233(n):

%o   return denom(sum((1-S(2)**(2-k))/factorial(k) for k in range(2,n+1)))

%o (Python)

%o from math import factorial

%o from fractions import Fraction

%o def a(n):

%o   s = sum(Fraction(2**k-4, 2**k*factorial(k)) for k in range(2, n+1))

%o   return s.denominator

%o print([a(n) for n in range(1, 21)]) # _Michael S. Branicky_, Feb 07 2021

%Y Cf. A248788, A341232 (numerators).

%K nonn,frac

%O 1,3

%A _Pontus von Brömssen_, Feb 07 2021