cp's OEIS Frontend

A174586 Number of n X n (0,1) matrices with two 1's in each row having positive permanent.

%I A174586 #30 Feb 07 2023 15:02:44
%S A174586 0,1,24,954,59040,5295150,651354480,105393619800,21717404916480,
%T A174586 5554438422838200,1726882980691176000,641506478978753110800,
%U A174586 280659563041747649760000,142843312073975729801785200,83684308104396267184700784000,55915646244745131440225950320000
%N A174586 Number of n X n (0,1) matrices with two 1's in each row having positive permanent.
%C A174586 a(n) is the normalized volume of the convex hull of (classical) parking functions of length n. - _Andrés R. Vindas-Meléndez_, Jan 13 2023
%D A174586 Vladimir Shevelev, On the permanent of the stochastic (0,1)-matrices with equal row sums, Izvestia Vuzov of the North-Caucasus region, Nature sciences 1 (1997), 21-38 (in Russian).
%H A174586 Aruzhan Amanbayeva and Danielle Wang, <a href="https://ecajournal.haifa.ac.il/Volume2022/ECA2022_S2A10.pdf">The convex hull of parking functions of length n</a>, Enumer. Comb. Appl. 2 (2022), no. 2, Paper No. S2R10, 1.
%H A174586 Mitsuki Hanada, John Lentfer, and Andrés R. Vindas-Meléndez, <a href="https://arxiv.org/abs/2212.06885">Generalized parking function polytopes</a>, arXiv:2212.06885 [math.CO], 2022.
%F A174586 a(2)=1, for n>=3, a(n) = A001499(n) + Sum_{k=1..n-2} (-1)^(k+1)*k!*(C(n,k))^2*(n-k)^k*a(n-k).
%F A174586 a(n) = n!*((n-1)/2^(n-1))*Sum_{i=0..n-2} (2i+1)!!*C(n-2,i)*(2n-1)^(n-i-2). [corrected by _John Lentfer_, Oct 05 2022]
%F A174586 For n>=2, a(n) = (n!/2^n)*Sum_{i=0..n} (2i-1)*(2i-1)!!*C(n,i)*(2n-1)^(n-i-1).
%F A174586 a(n) = Gamma(3/4)*(sqrt(2)*Pi*e)^(-1/2)*n!*n^(n-1/4)*(1+O(n^((-1/4)+epsilon) with arbitrary small epsilon>0 for sufficiently large n.
%t A174586 Table[n!/2^n * Sum[(2*i-1)*(2*i-1)!!*Binomial[n,i]*(2n-1)^(n-i-1),{i,0,n}],{n,1,20}] (* _Vaclav Kotesovec_, Nov 30 2017 *)
%Y A174586 Cf. A001499, A007107, A082491.
%K A174586 nonn
%O A174586 1,3
%A A174586 _Vladimir Shevelev_, Mar 23 2010