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 A386957 #23 Aug 21 2025 09:59:03
%S A386957 1,11,114,1163,11806,119646,1211820,12271179,124251318,1258065866,
%T A386957 12737997724,128972535582,1305848105836,13221716621852,
%U A386957 133869898347264,1355432788629963,13723757247851046,138953043155444562,1406899565919247884,14244858120395937738,144229188529316725956
%N A386957 a(n) = Sum_{k=0..n} 8^k * binomial(2*n+1,n-k).
%H A386957 Vincenzo Librandi, <a href="/A386957/b386957.txt">Table of n, a(n) for n = 0..400</a>
%F A386957 a(n) = [x^n] 1/((1-9*x) * (1-x)^(n+1)).
%F A386957 a(n) = Sum_{k=0..n} 9^k * (-8)^(n-k) * binomial(2*n+1,k) * binomial(2*n-k,n-k).
%F A386957 a(n) = Sum_{k=0..n} 9^k * binomial(2*n-k,n-k).
%F A386957 G.f.: 2/( sqrt(1-4*x) * (9*sqrt(1-4*x)-7) ).
%F A386957 D-finite with recurrence 8*n*a(n) +(-113*n+16)*a(n-1) +162*(2*n-1)*a(n-2)=0. - _R. J. Mathar_, Aug 21 2025
%t A386957 Table[Sum[8^k*Binomial[2*n+1,n-k],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Aug 14 2025 *)
%o A386957 (PARI) a(n) = sum(k=0, n, 8^k*binomial(2*n+1, n-k));
%o A386957 (Magma) [&+[8^k * Binomial(2*n+1, n-k): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, Aug 14 2025
%Y A386957 Cf. A000302, A000984, A026641, A141223, A377011.
%Y A386957 Cf. A386958, A386960.
%K A386957 nonn
%O A386957 0,2
%A A386957 _Seiichi Manyama_, Aug 11 2025