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%I #12 Oct 20 2014 17:15:14
%S 0,1,-1,9,-47,299,-1953,13231,-91729,647433,-4633499,33531761,
%T -244884159,1802040241,-13346305519,99392117841,-743734839215,
%U 5588564785067,-42148760792553,318928716891883,-2420342154102853,18416484881248743,-140466988872011009,1073705008744247231,-8223501739695527745
%N a(n) = Sum_{k=0..n-1} (-1)^k*A000172(k).
%H Z.-W. Sun, <a href="http://arxiv.org/abs/1112.1034">Congruences for Franel numbers</a>, arXiv preprint arXiv:1112.1034, 2011. See Eq. 1.5.
%F Conjecture: (n-1)^2*a(n) +(2*n-3)*(3*n-5)*a(n-1) +(-15*n^2+53*n-48)*a(n-2) +8*(n-2)^2*a(n-3)=0. - _R. J. Mathar_, Nov 28 2013
%F a(n) ~ (-1)^(n+1) * sqrt(3) * 2^(3*n+1) / (27*Pi*n). - _Vaclav Kotesovec_, Jan 31 2014
%t Flatten[{0,Table[Sum[(-1)^k*Sum[Binomial[k,j]^3,{j,0,k}],{k,0,n-1}],{n,1,20}]}] (* _Vaclav Kotesovec_, Jan 31 2014 *)
%K sign
%O 0,4
%A _N. J. A. Sloane_, Feb 16 2012
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