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 A383499 #22 May 05 2025 07:18:30
%S A383499 1,2,9,22,71,186,537,1434,3957,10586,28603,76266,203767,540986,
%T A383499 1435533,3796050,10026015,26422350,69544765,182759750,479731113,
%U A383499 1257750486,3294264627,8619879726,22535782953,58869786162,153671378139,400861115498,1045005290059,2722601576322
%N A383499 Expansion of 1/sqrt( (1-x) * (1-x-4*x^2)^3 ).
%F A383499 a(n) = Sum_{k=0..floor(n/2)} (2*k+1) * binomial(2*k,k) * binomial(n-k+1,k+1).
%F A383499 a(n) ~ sqrt(n/Pi) * ((1 + sqrt(17))/2)^(n + 5/2) / 17^(3/4). - _Vaclav Kotesovec_, May 05 2025
%o A383499 (PARI) a(n) = sum(k=0, n\2, (2*k+1)*binomial(2*k, k)*binomial(n-k+1, k+1));
%Y A383499 Cf. A383254, A383503.
%Y A383499 Cf. A026569, A377204.
%K A383499 nonn
%O A383499 0,2
%A A383499 _Seiichi Manyama_, May 05 2025