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%I #13 Feb 12 2019 12:05:16
%S 0,0,-2,38,-466,5070,-51230,495394,-4647646,42658722,-385096770,
%T 3431429230,-30256897090,264500216510,-2295570216930,19801160761630,
%U -169902404575970,1451166299240222,-12344920792691958,104644181977065306,-884232602452034390,7450498211688604010,-62617113713498946622,525042133132770041538
%N a(n) = Sum_{k=0..n-1} (-1)^k*k^2*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.
%t a172[n_] := Sum[Binomial[2k, n] Binomial[2k, k] Binomial[2(n-k), n-k], {k, 0, n}]/2^n;
%t a[n_] := Sum[(-1)^k k^2 a172[k], {k, 0, n-1}];
%t Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Feb 12 2019 *)
%K sign
%O 0,3
%A _N. J. A. Sloane_, Feb 16 2012
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