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 A377239 #8 May 03 2025 04:14:11
%S A377239 1,2,2,8,22,80,268,976,3494,12896,47556,177744,666236,2515104,9525976,
%T A377239 36240032,138269958,529193152,2030242708,7807266512,30082317460,
%U A377239 116126074400,449014896040,1738805527520,6742758295900,26180338089280,101769629532968,396031222808096,1542673037902904
%N A377239 Expansion of sqrt(1 + 4*x/sqrt(1 - 4*x)).
%F A377239 a(n) = 4^n * Sum_{k=0..n} binomial(1/2,k) * binomial(n-k/2-1,n-k).
%F A377239 a(n) ~ 2^(2*n) / (Gamma(1/4) * n^(3/4)) * (1 - Gamma(1/4)^2 / (Pi*2^(7/2)*sqrt(n))). - _Vaclav Kotesovec_, May 03 2025
%o A377239 (PARI) a(n) = 4^n*sum(k=0, n, binomial(1/2, k)*binomial(n-k/2-1, n-k));
%Y A377239 Cf. A377240.
%K A377239 nonn
%O A377239 0,2
%A A377239 _Seiichi Manyama_, Oct 21 2024