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 A382471 #20 Apr 10 2025 14:57:13
%S A382471 1,5,20,125,610,2611,10815,42610,161005,590155,2106362,7348265,
%T A382471 25141430,84569395,280246795,916465742,2961805180,9470735650,
%U A382471 29994694130,94172180660,293326457342,907028460410,2786036875580,8505001839950,25815678641935,77945771624609
%N A382471 a(n) = Sum_{k=0..n} binomial(k+4,4) * binomial(2*k,2*n-2*k).
%H A382471 Vincenzo Librandi, <a href="/A382471/b382471.txt">Table of n, a(n) for n = 0..400</a>
%H A382471 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-55,172,-250,100,-365,510,-29,510,-365,100,-250,172,-55,50,-35,10,-1).
%F A382471 G.f.: (Sum_{k=0..2} 4^k * binomial(5,2*k) * (1-x-x^2)^(5-2*k) * x^(3*k)) / ((1-x-x^2)^2 - 4*x^3)^5.
%t A382471 Table[Sum[Binomial[k+4,4]*Binomial[2*k,2*n-2*k],{k,0,n}],{n,0,30}] (* _Vincenzo Librandi_, Apr 10 2025 *)
%o A382471 (PARI) a(n) = sum(k=0, n, binomial(k+4, 4)*binomial(2*k, 2*n-2*k));
%o A382471 (PARI) my(N=4, M=30, x='x+O('x^M), X=1-x-x^2, Y=3); Vec(sum(k=0, (N+1)\2, 4^k*binomial(N+1, 2*k)*X^(N+1-2*k)*x^(Y*k))/(X^2-4*x^Y)^(N+1))
%o A382471 (Magma) [&+[Binomial(k+4,4) * Binomial(2*k,2*n-2*k): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Apr 10 2025
%Y A382471 Cf. A108479, A381421, A382230, A382470, A382472, A382473, A382474.
%Y A382471 Cf. A034839, A377152.
%K A382471 nonn,easy
%O A382471 0,2
%A A382471 _Seiichi Manyama_, Mar 28 2025