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 A372005 #12 Apr 19 2024 02:26:58
%S A372005 1,4,-4,0,136,-1152,5152,0,-230560,2267136,-11355008,0,594412800,
%T A372005 -6184304640,32458736640,0,-1828185954816,19583341166592,
%U A372005 -105435193825280,0,6195266435870720,-67554137604096000,369569533686562816,0,-22322916873246359552,246346071588005216256
%N A372005 G.f. A(x) satisfies A(x) = ( 1 + 16*x*A(x)*(1 + x*A(x)) )^(1/4).
%F A372005 a(n) = (1/(n+1)) * Sum_{k=0..n} 16^k * binomial(n/4+1/4,k) * binomial(k,n-k).
%F A372005 a(4*n+3) = 0 for n >= 0.
%F A372005 a(n) = 16^n*binomial((n+1)/4, n)*hypergeom([(1-n)/2, -n/2], [(5-3*n)/4], 1/4)/(n+1). - _Stefano Spezia_, Apr 18 2024
%o A372005 (PARI) a(n) = sum(k=0, n, 16^k*binomial(n/4+1/4, k)*binomial(k, n-k))/(n+1);
%Y A372005 Cf. A372004, A372006.
%K A372005 sign
%O A372005 0,2
%A A372005 _Seiichi Manyama_, Apr 15 2024