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 A358114 #13 Jan 25 2023 09:26:10
%S A358114 1,24,608,16128,443904,12570624,363708416,10694295552,318301929472,
%T A358114 9562594738176,289380790960128,8807948507676672,269349580129173504,
%U A358114 8268747111256817664,254668380196759928832,7865254221563736096768,243493498808268962660352,7553805204299934842486784
%N A358114 a(n) = [x^n] (16*x*(32*x - 3) + 1)^(-1/2).
%F A358114 a(n) = 16^n * hypergeom([1/2, -n], [1], -1).
%F A358114 D-finite with recurrence a(n) = (24*(2*n - 1)*a(n - 1) - 512*(n - 1)*a(n - 2)) / n for n >= 2.
%F A358114 a(n) ~ 2^(5*n + 1/2) / sqrt(Pi*n). - _Vaclav Kotesovec_, Nov 12 2022
%F A358114 a(n) = 4^n*A098410(n). - _R. J. Mathar_, Jan 25 2023
%p A358114 ogf := (16*x*(32*x - 3) + 1)^(-1/2): ser := series(ogf, x, 20):
%p A358114 seq(coeff(ser, x, n), n = 0..17);
%t A358114 a[n_] := 16^n * HypergeometricPFQ[{1/2, -n}, {1}, -1]; Array[a, 18, 0] (* _Amiram Eldar_, Nov 12 2022 *)
%Y A358114 Cf. A098430.
%K A358114 nonn
%O A358114 0,2
%A A358114 _Peter Luschny_, Nov 12 2022