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 A382473 #22 Apr 11 2025 07:59:04
%S A382473 1,7,35,252,1498,7602,36498,165600,713769,2957647,11850223,46111352,
%T A382473 174956250,649284286,2362771938,8449241836,29744151416,103237104740,
%U A382473 353744829032,1198001464940,4013905507150,13316690882670,43780154987030,142726581203640
%N A382473 a(n) = Sum_{k=0..n} binomial(k+6,6) * binomial(2*k,2*n-2*k).
%H A382473 Vincenzo Librandi, <a href="/A382473/b382473.txt">Table of n, a(n) for n = 0..500</a>
%H A382473 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (14, -77, 210, -336, 602, -1435, 2018, -1981, 4312, -5894, 3360, -7721, 9562, -3079, 9562, -7721, 3360, -5894, 4312, -1981, 2018, -1435, 602, -336, 210, -77, 14, -1).
%F A382473 G.f.: (Sum_{k=0..3} 4^k * binomial(7,2*k) * (1-x-x^2)^(7-2*k) * x^(3*k)) / ((1-x-x^2)^2 - 4*x^3)^7.
%t A382473 Table[Sum[Binomial[k+6,6]*Binomial[2*k,2*n-2*k],{k,0,n}],{n,0,30}] (* _Vincenzo Librandi_, Apr 11 2025 *)
%o A382473 (PARI) a(n) = sum(k=0, n, binomial(k+6, 6)*binomial(2*k, 2*n-2*k));
%o A382473 (PARI) my(N=6, 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 A382473 (Magma) [&+[Binomial(k+6, 6) * Binomial(2*k, 2*n-2*k): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Apr 11 2025
%Y A382473 Cf. A108479, A381421, A382230, A382470, A382471, A382472, A382474.
%Y A382473 Cf. A034839, A377158.
%K A382473 nonn,easy
%O A382473 0,2
%A A382473 _Seiichi Manyama_, Mar 28 2025