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%I #15 Mar 30 2018 02:42:36
%S 0,3,18,111,750,5403,40572,313407,2471166,19791003,160459068,
%T 1313922063,10847561088,90174127683,754009158018,6336733626111,
%U 53489159252670,453258909448635,3854034482891724,32871004555812111,281127047928811200,2410285909684370787,20711470169495359602,178337708176330555839
%N Partial sums of A002893.
%H Z.-W. Sun, <a href="http://arxiv.org/abs/1112.1034">Congruences for Franel numbers</a>, arXiv preprint arXiv:1112.1034, 2011.
%F n^2*a(n) +(-11*n^2+10*n-3)*a(n-1) +(19*n^2-28*n+12)*a(n-2) -9*(n-1)^2*a(n-3)=0. - _R. J. Mathar_, Aug 25 2013
%F a(n) ~ 3^(2*n + 7/2) / (32*Pi*n). - _Vaclav Kotesovec_, Mar 30 2018
%t Table[Sum[HypergeometricPFQ[{1/2, -k, -k}, {1, 1}, 4], {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Mar 30 2018 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Feb 16 2012
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