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

1, 16, 480, 17920, 752640, 34062336, 1623638016, 80408739840, 4100845731840, 214072431738880, 11388653368508416, 615465127495335936, 33704042696173158400, 1866685441634205696000, 104401050057113075712000, 5889038054986331298201600, 334693662791723162114457600

Offset: 0

Author

Peter Luschny, Feb 03 2015

Keywords

• nonn

Crossrefs

Cf. A172392, A254632.

Programs

Maple

a := n -> 16^n*coeff(simplify(hypergeom([3/2, -2*n], [3], -x)), x, n):
seq(a(n), n=0..16);
a_list := len -> seq(coeff(series(hypergeom([1/2, 3/2],[3],64*x),x,len+1),x,n),n=0..len);
a_list(16);

Formula

a(n) = 4^n*C(2*n,n)*C(2*n+2,n+1)/(n+2).

a(n) = (2^(6*n+2)*Gamma(n+1/2)*Gamma(n+3/2))/(Pi*Gamma(n+1)*Gamma(n+3)).

a(n) = A254632(2*n,n).

a(n) = 4^n * A172392(n).

a(n) = [x^n]hypergeom([1/2, 3/2], [3], 64*x).

a(n) = a(n-1)*( 16*(4*n^2-1)/(n*(n+2)) ) for n >= 1.