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%I #17 Apr 05 2019 10:43:53
%S 0,0,0,0,31,315,2112,11830,60060,287028,1317840,5883768,25741485,
%T 110921525,472431960,1993896450,8354335080,34799391000,144259293600,
%U 595644532560,2451231964350,10059146122662,41181227878560,168246990214380,686162857445736,2794089011606200,11362424624634720,46152024284293200,187266363241782825
%N a(n) = 31*binomial(2*n,n-4) + Sum_{i=1..n-4} binomial(2*n,n-4-i)*(4+i).
%H Olivia Beckwith, Victor Luo, Stephen J. Miller, Karen Shen, Nicholas Triantafillou, <a href="http://arxiv.org/abs/1112.3719">Distribution of Eigenvalues of Weighted, Structured Matrix Ensembles</a>, arXiv preprint arXiv:1112.3719 [math.PR], 2011-2012.
%H Olivia Beckwith, Victor Luo, Stephen J. Miller, Karen Shen, Nicholas Triantafillou, <a href="https://www.emis.de/journals/INTEGERS/papers/p21/p21.Abstract.html">Distribution of Eigenvalues of Weighted, Structured Matrix Ensembles</a>, Electronic Journal of Combinatorial Number Theory, Volume 15 (2015) #A21.
%F Conjecture: 558*(n-4)*(n+4)*a(n) +7*(-631*n^2+777*n+4600)*a(n-1) +4370*(n-1)*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Aug 08 2012
%p f:=n->31*binomial(2*n,n-4)+add(binomial(2*n,n-4-i)*(4+i),i=1..n-4);
%p [seq(f(n),n=0..40)];
%t Table[31*Binomial[2n,n-4]+Sum[Binomial[2n,n-4-i](4+i),{i,n-4}],{n,0,30}] (* _Harvey P. Dale_, May 24 2016 *)
%o (PARI) a(n) = 31*binomial(2*n,n-4) + sum(i=1, n-4, binomial(2*n,n-4-i)*(4+i)); \\ _Michel Marcus_, Apr 05 2019
%Y Cf. A182026.
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Apr 06 2012
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