login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numerator of the probability that the sum of n uniform picks on [0,1] is first greater than 2 (i.e., the sum of n-1 is not).
2

%I #10 Apr 12 2022 03:25:55

%S 0,0,1,1,11,13,19,1,247,251,1013,509,1361,1363,16369,2047,65519,851,

%T 233,14563,209711,29959,46091,1048573,5592397,5592401,67108837,

%U 1342177,20648879,268435441,357913931,22369621,4294967263,4294967279

%N Numerator of the probability that the sum of n uniform picks on [0,1] is first greater than 2 (i.e., the sum of n-1 is not).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UniformSumDistribution.html">Uniform Sum Distribution</a>.

%F a(n) = numerator((n-2)*(2^(n-1)-n)/n!). - _Amiram Eldar_, Apr 12 2022

%e 0, 0, 1/6, 1/3, 11/40, 13/90, 19/336, ...

%t a[n_] := Numerator[(n - 2)*(2^(n - 1) - n)/n!]; Array[a, 50] (* _Amiram Eldar_, Apr 12 2022 *)

%Y Cf. A090138 (denominators).

%K nonn,frac

%O 1,5

%A _Eric W. Weisstein_, Nov 22 2003