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 A386960 #22 Aug 13 2025 15:00:29
%S A386960 1,10,102,1036,10502,106380,1077276,10908096,110447046,1118286172,
%T A386960 11322685172,114642332232,1160754172316,11752638152824,
%U A386960 118995469654968,1204829162684136,12198895398209862,123513816397462524,1250577392936568708,12662096110945862856,128203723152486704052
%N A386960 a(n) = Sum_{k=0..n} 8^k * binomial(2*n,n-k).
%H A386960 Vincenzo Librandi, <a href="/A386960/b386960.txt">Table of n, a(n) for n = 0..400</a>
%F A386960 a(n) = [x^n] 1/((1-9*x) * (1-x)^n).
%F A386960 a(n) = Sum_{k=0..n} 9^k * (-8)^(n-k) * binomial(2*n,k) * binomial(2*n-k-1,n-k).
%F A386960 a(n) = Sum_{k=0..n} 9^k * binomial(2*n-k-1,n-k).
%F A386960 G.f.: (1+sqrt(1-4*x))/( sqrt(1-4*x) * (9*sqrt(1-4*x)-7) ).
%t A386960 Table[Sum[8^k*Binomial[2*n,n-k],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Aug 13 2025 *)
%o A386960 (PARI) a(n) = sum(k=0, n, 8^k*binomial(2*n, n-k));
%o A386960 (Magma) [&+[8^k * Binomial(2*n, n-k): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Aug 13 2025
%Y A386960 Cf. A032443, A072547, A088218, A100192, A100193.
%K A386960 nonn
%O A386960 0,2
%A A386960 _Seiichi Manyama_, Aug 11 2025