A341233 - OEIS

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A341233

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

1, 1, 12, 96, 320, 3840, 161280, 516096, 46448640, 185794560, 2270822400, 163499212800, 1821848371200, 51011754393600, 10712468422656000, 9794256843571200, 555007887802368000, 139861987726196736000, 1449478781889675264000, 49059281848573624320000

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..20.

FORMULA

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

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

EXAMPLE

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

PROG

(Python)

from sympy import denom, S, factorial

def A341233(n):

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

print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Feb 07 2021

CROSSREFS

Cf. A248788, A341232 (numerators).

Sequence in context: A204630 A192848 A229561 * A120658 A121627 A138162

Adjacent sequences: A341230 A341231 A341232 * A341234 A341235 A341236

KEYWORD

nonn,frac

AUTHOR

Pontus von Brömssen, Feb 07 2021

STATUS

approved