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 A382474 #18 Apr 22 2025 21:54:55
%S A382474 1,8,44,336,2166,11832,60576,292248,1334817,5840296,24637976,
%T A382474 100684376,400255050,1553016960,5897388492,21967711160,80425346844,
%U A382474 289868771928,1029979010972,3612517052608,12520285820362,42919328903928,145643017892472,489606988741128
%N A382474 a(n) = Sum_{k=0..n} binomial(k+7,7) * binomial(2*k,2*n-2*k).
%H A382474 Vincenzo Librandi, <a href="/A382474/b382474.txt">Table of n, a(n) for n = 0..500</a>
%H A382474 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (16, -104, 352, -708, 1232, -2800, 5168, -6122, 9728, -18008, 16816, -19152, 37744, -27096, 24960, -50611, 24960, -27096, 37744, -19152, 16816, -18008, 9728, -6122, 5168, -2800, 1232, -708, 352, -104, 16, -1).
%F A382474 G.f.: (Sum_{k=0..4} 4^k * binomial(8,2*k) * (1-x-x^2)^(8-2*k) * x^(3*k)) / ((1-x-x^2)^2 - 4*x^3)^8.
%t A382474 Table[Sum[Binomial[k+7,7]*Binomial[2*k,2*n-2*k],{k,0,n}],{n,0,30}] (* _Vincenzo Librandi_, Apr 22 2025 *)
%o A382474 (PARI) a(n) = sum(k=0, n, binomial(k+7, 7)*binomial(2*k, 2*n-2*k));
%o A382474 (PARI) my(N=7, 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 A382474 (Magma) [&+[Binomial(k+7, 7) * Binomial(2*k, 2*n-2*k): k in [0..n]]: n in [0..29]]; // _Vincenzo Librandi_, Apr 22 2025
%Y A382474 Cf. A108479, A381421, A382230, A382470, A382471, A382472, A382473.
%Y A382474 Cf. A034839, A377159.
%K A382474 nonn,easy
%O A382474 0,2
%A A382474 _Seiichi Manyama_, Mar 28 2025