A358114 - OEIS

%I #13 Jan 25 2023 09:26:10

%S 1,24,608,16128,443904,12570624,363708416,10694295552,318301929472,

%T 9562594738176,289380790960128,8807948507676672,269349580129173504,

%U 8268747111256817664,254668380196759928832,7865254221563736096768,243493498808268962660352,7553805204299934842486784

%N a(n) = [x^n] (16*x*(32*x - 3) + 1)^(-1/2).

%F a(n) = 16^n * hypergeom([1/2, -n], [1], -1).

%F D-finite with recurrence a(n) = (24*(2*n - 1)*a(n - 1) - 512*(n - 1)*a(n - 2)) / n for n >= 2.

%F a(n) ~ 2^(5*n + 1/2) / sqrt(Pi*n). - _Vaclav Kotesovec_, Nov 12 2022

%F a(n) = 4^n*A098410(n). - _R. J. Mathar_, Jan 25 2023

%p ogf := (16*x*(32*x - 3) + 1)^(-1/2): ser := series(ogf, x, 20):

%p seq(coeff(ser, x, n), n = 0..17);

%t a[n_] := 16^n * HypergeometricPFQ[{1/2, -n}, {1}, -1]; Array[a, 18, 0] (* _Amiram Eldar_, Nov 12 2022 *)

%Y Cf. A098430.

%K nonn

%O 0,2

%A _Peter Luschny_, Nov 12 2022