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 A382472 #19 Apr 11 2025 01:26:18
%S A382472 1,6,27,182,987,4620,20678,87732,355095,1387462,5258967,19416222,
%T A382472 70086803,248046540,862694058,2954279732,9977518122,33278815920,
%U A382472 109749059308,358231786128,1158357919194,3713416860580,11810098024410,37285901203740,116917784689237
%N A382472 a(n) = Sum_{k=0..n} binomial(k+5,5) * binomial(2*k,2*n-2*k).
%H A382472 Vincenzo Librandi, <a href="/A382472/b382472.txt">Table of n, a(n) for n = 0..500</a>
%H A382472 <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (12,-54,112,-141,312,-674,588,-714,1812,-1134,888,-2741,888,-1134,1812,-714,588,-674,312,-141,112,-54,12,-1).
%F A382472 G.f.: (Sum_{k=0..3} 4^k * binomial(6,2*k) * (1-x-x^2)^(6-2*k) * x^(3*k)) / ((1-x-x^2)^2 - 4*x^3)^6.
%t A382472 Table[Sum[Binomial[k+5,5]*Binomial[2*k,2*n-2*k],{k,0,n}],{n,0,30}] (* _Vincenzo Librandi_, Apr 11 2025 *)
%o A382472 (PARI) a(n) = sum(k=0, n, binomial(k+5, 5)*binomial(2*k, 2*n-2*k));
%o A382472 (PARI) my(N=5, 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 A382472 (Magma) [&+[Binomial(k+5, 5) * Binomial(2*k, 2*n-2*k): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Apr 11 2025
%Y A382472 Cf. A108479, A381421, A382230, A382470, A382471, A382473, A382474.
%Y A382472 Cf. A034839, A377153.
%K A382472 nonn,easy
%O A382472 0,2
%A A382472 _Seiichi Manyama_, Mar 28 2025