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 A086025 #22 Jan 14 2025 10:26:48
%S A086025 1,37,478,3614,19490,82994,296438,923702,2580071,6588075,15606084,
%T A086025 34685508,72976852,146387476,281597860,521971876,936053677,1629533233,
%U A086025 2761788434,4568378450,7391175350,11718183750,18235516650,27894475050,41997225075,62305185111
%N A086025 a(n) = Sum_{i=1..n} C(i+4,5)^2.
%H A086025 T. D. Noe, <a href="/A086025/b086025.txt">Table of n, a(n) for n = 1..1000</a>
%H A086025 John Engbers and Christopher Stocker, <a href="http://epublications.marquette.edu/mscs_fac/456/">Two Combinatorial Proofs of Identities Involving Sums of Powers of Binomial Coefficients</a>, Integers 16 (2016), #A58.
%H A086025 Feihu Liu, Guoce Xin, and Chen Zhang, <a href="https://arxiv.org/abs/2412.18744">Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS</a>, arXiv:2412.18744 [math.CO], 2024. See p. 13.
%H A086025 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495, 220,-66,12,-1).
%F A086025 From _R. J. Mathar_, Jun 16 2010: (Start)
%F A086025 G.f.: x*(1+x)*(x^4+24*x^3+76*x^2+24*x+1)/(x-1)^12.
%F A086025 a(n) = n*(2*n+5)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*(63*n^4 +630*n^3 +1855*n^2 +1400*n +12) / 19958400. (End)
%t A086025 Table[n*(2*n+5)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*(63*n^4 +630*n^3 +1855*n^2 +1400*n +12)/19958400, {n,1,30}] (* _G. C. Greubel_, Nov 22 2017 *)
%t A086025 LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{1,37,478,3614,19490,82994,296438,923702,2580071,6588075,15606084,34685508},30] (* _Harvey P. Dale_, Dec 22 2024 *)
%o A086025 (PARI) for(n=1,30, print1(sum(i=1,n, binomial(i+4,5)^2), ", ")) \\ _G. C. Greubel_, Nov 22 2017
%o A086025 (Magma) [n*(2*n+5)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*(63*n^4 +630*n^3 +1855*n^2 +1400*n +12)/19958400: n in [1..30]]; // _G. C. Greubel_, Nov 22 2017
%Y A086025 Cf. A087127, A024166, A085438, A085439, A085440, A085441, A085442, A086020, A086021, A086022, A086023, A086024, A086026, A086027, A086028, A086029, A086030.
%K A086025 easy,nonn
%O A086025 1,2
%A A086025 _André F. Labossière_, Jul 11 2003
%E A086025 More terms from _R. J. Mathar_, Jun 16 2010