OFFSET
0,2
COMMENTS
Combinatorial interpretation welcome.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f. is equivalent to -3*( 1+2*x -2F1(-1/2,-1/2;2;16*x) ) /(4*x^2).
a(n) = 3/((n+3)*(n+2)^2)*(2*n+2)!^2/(n+1)!^4 = 3/(n+3)* Catalan(n+1)^2. - Peter Bala, Mar 28 2018
D-finite with recurrence (n+3)*(n+2)*a(n) -4*(2*n+1)^2*a(n-1)=0. - R. J. Mathar, Feb 08 2021
MAPLE
seq(3/((n+3)*(n+2)^2)*binomial(2*n+2, n+1)^2, n = 0..20); # Peter Bala, Mar 28 2018
MATHEMATICA
CoefficientList[Series[HypergeometricPFQ[{1, 3/2, 3/2}, {3, 4}, 16*x], {x, 0, 20}],
x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Feb 16 2011
STATUS
approved