OFFSET
0,1
FORMULA
a(n) = binomial(4n+3, 2n+2). - Emeric Deutsch, Dec 09 2004
From Peter Bala, Mar 19 2023: (Start)
a(n) = (1/2)*Sum_{k = 0..2*n+2} binomial(2*n+2,k)^2.
a(n) = (1/2)*hypergeom([-2 - 2*n, -2 - 2*n], [1], 1).
a(n) = 2*(4*n + 1)*(4*n + 3)/((n + 1)*(2*n + 1)) * a(n-1). (End)
From Peter Bala, Mar 28 2023
a(n) = (1/(2*n + 2))*Sum_{k = 0..2*n+2} k*binomial(2*n+2,k)^2.
a(n) = 2*(n + 1)*hypergeom([-1 - 2*n, -1 - 2*n], [2], 1). (End)
MAPLE
a:=n->binomial(4*n+3, 2*n+2): seq(a(n), n=0..19);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 20 2004
EXTENSIONS
More terms from Emeric Deutsch, Dec 09 2004
STATUS
approved