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%I #18 Oct 31 2018 11:53:39
%S 0,3,33,312,2868,26133,237147,2146992,19409064,175287597,1581968247,
%T 14270061192,128673729492,1159919095227,10453609519917,94194476541312,
%U 848633286566256,7644719039897661,68858679361873263,620181110747360616,5585301978207342396,50297638075074093723,452923691790915847653
%N a(n) = Sum_{k=0..n} k*A002893(k).
%H Z.-W. Sun, <a href="http://arxiv.org/abs/1112.1034">Congruences for Franel numbers</a>, arXiv preprint arXiv:1112.1034, 2011.
%F Conjecture: n*(n-1)*a(n) +(-14*n^2+23*n-12)*a(n-1) +(52*n^2-151*n+120)*a(n-2) +3*(-22*n^2+79*n-72)*a(n-3) +27*(n-2)^2*a(n-4)=0. - _R. J. Mathar_, Nov 28 2013
%t a[n_] := Sum[k Sum[Binomial[k, j]^2 Binomial[2j, j], {j, 0, k}], {k, 0, n}];
%t Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, Oct 31 2018 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Feb 16 2012
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