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A254633 a(n) = 16^n*[x^n]hypergeometric([3/2, -2*n], [3], -x).

%I A254633 #18 Jun 11 2024 01:36:48
%S A254633 1,16,480,17920,752640,34062336,1623638016,80408739840,4100845731840,
%T A254633 214072431738880,11388653368508416,615465127495335936,
%U A254633 33704042696173158400,1866685441634205696000,104401050057113075712000,5889038054986331298201600,334693662791723162114457600
%N A254633 a(n) = 16^n*[x^n]hypergeometric([3/2, -2*n], [3], -x).
%F A254633 a(n) = 4^n*C(2*n,n)*C(2*n+2,n+1)/(n+2).
%F A254633 a(n) = (2^(6*n+2)*Gamma(n+1/2)*Gamma(n+3/2))/(Pi*Gamma(n+1)*Gamma(n+3)).
%F A254633 a(n) = A254632(2*n,n).
%F A254633 a(n) = 4^n * A172392(n).
%F A254633 a(n) = [x^n]hypergeom([1/2, 3/2], [3], 64*x).
%F A254633 a(n) = a(n-1)*( 16*(4*n^2-1)/(n*(n+2)) ) for n >= 1.
%p A254633 a := n -> 16^n*coeff(simplify(hypergeom([3/2, -2*n], [3], -x)), x, n):
%p A254633 seq(a(n), n=0..16);
%p A254633 a_list := len -> seq(coeff(series(hypergeom([1/2, 3/2],[3],64*x),x,len+1),x,n),n=0..len);
%p A254633 a_list(16);
%Y A254633 Cf. A172392, A254632.
%K A254633 nonn
%O A254633 0,2
%A A254633 _Peter Luschny_, Feb 03 2015