cp's OEIS Frontend

A293458 Numerator of probability that a permutation of elements of some subset of set {1,2,...,n} is a permutation of elements of some set of the form 1..k, k <= n.

%I A293458 #28 Feb 11 2020 02:04:13
%S A293458 1,1,5,17,77,437,2957,23117,204557,2018957,21977357,261478157,
%T A293458 3374988557,46964134157,700801318157,11162196262157,189005910310157,
%U A293458 3390192763174157,64212742967590157,1280663747055910157,26826134832910630157,588826498721714470157
%N A293458 Numerator of probability that a permutation of elements of some subset of set {1,2,...,n} is a permutation of elements of some set of the form 1..k, k <= n.
%C A293458 The number of all permutations of elements of sets {1..k}, k <= n, is b(n) = Sum_{k=0..n} k! while the number of all permutations of elements of all subsets of set {1,2..n} is c(n) = Sum_{k=0..n} binomial(n,k)!. So the required probability (in a sample space) is b(n)/c(n), n >= 1 (after reduction of the fractions).
%C A293458 Apparently a(n) = A014288(n) for n > 2. - _Georg Fischer_, Oct 23 2018
%H A293458 Amiram Eldar, <a href="/A293458/b293458.txt">Table of n, a(n) for n = 1..30</a>
%t A293458 a[n_] := Numerator[Sum[k!, {k, 0, n}]/Sum[Binomial[n, k]!, {k, 0, n}]]; Array[a, 25] (* _Amiram Eldar_, Sep 21 2019 *)
%o A293458 (PARI) a(n) = numerator(sum(k=0, n, k!)/sum(k=0, n, binomial(n,k)!)); \\ _Michel Marcus_, Oct 12 2017
%Y A293458 Denominators are in A293459.
%Y A293458 Cf. A014288.
%K A293458 nonn,frac
%O A293458 1,3
%A A293458 _Vladimir Shevelev_, Oct 09 2017
%E A293458 More terms from _Peter J. C. Moses_, Oct 09 2017