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%I #16 Oct 31 2018 11:45:47
%S 0,0,-2,18,-150,1234,-10026,81078,-653642,5259654,-42268734,339383866,
%T -2723191254,21839901546,-175088593334,1403249333706,-11243655022134,
%U 90073138966378,-721461395853162,5777933202466686,-46268213346433298,370468327360598622,-2966084621457856170,23745699326099825110
%N a(n) = Sum_{k=0..n-1} (-1)^k*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. 1.6.
%F Conjecture: (n-1)*(n-2)*a(n) +2*(n^2+3*n-9)*a(n-1) +3*(-13*n^2+63*n-80)*a(n-2) +4*(17*n^2-96*n+136)*a(n-3) -32*(n-3)^2*a(n-4)=0. - _R. J. Mathar_, Nov 28 2013
%t a[n_] := Sum[(-1)^k k Sum[Binomial[k, j]^3, {j, 0, k}], {k, 0, n-1}];
%t Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Oct 31 2018 *)
%K sign
%O 0,3
%A _N. J. A. Sloane_, Feb 16 2012
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