This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A207321 #22 Jan 12 2025 16:56:25
%S A207321 0,3,18,111,750,5403,40572,313407,2471166,19791003,160459068,
%T A207321 1313922063,10847561088,90174127683,754009158018,6336733626111,
%U A207321 53489159252670,453258909448635,3854034482891724,32871004555812111,281127047928811200,2410285909684370787,20711470169495359602,178337708176330555839
%N A207321 Partial sums of A002893 with A002893(0)=0.
%H A207321 Z.-W. Sun, <a href="http://arxiv.org/abs/1112.1034">Congruences for Franel numbers</a>, arXiv preprint arXiv:1112.1034, 2011.
%F A207321 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 A207321 a(n) ~ 3^(2*n + 7/2) / (32*Pi*n). - _Vaclav Kotesovec_, Mar 30 2018
%F A207321 a(n) = A174123(n) - 1. - _Sean A. Irvine_, Jan 12 2025
%t A207321 Table[Sum[HypergeometricPFQ[{1/2, -k, -k}, {1, 1}, 4], {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Mar 30 2018 *)
%Y A207321 Cf. A002893, A174123.
%K A207321 nonn
%O A207321 0,2
%A A207321 _N. J. A. Sloane_, Feb 16 2012
%E A207321 Name clarified by _Sean A. Irvine_, Jan 12 2025