OFFSET
0,2
COMMENTS
Member of Bober's second infinite family of integral factorial ratio sequences with a=5 and b=3 (see equation 11 at p. 16 in Bober).
LINKS
Jonathan W. Bober, Factorial ratios, hypergeometric series, and a family of step functions, Journal of the London Mathematical Society, Vol. 79, No. 2 (2009), pp. 422-444; arXiv preprint, arXiv:0709.1977 [math.NT], 2007.
FORMULA
a(n) = 10*(10*n - 1)*(10*n - 3)*(10*n - 7)*(10*n - 9)/(3*n*(2*n - 1)*(6*n - 1)*(6*n - 5))*a(n-1).
a(n) ~ 2^(2*n-1) * 5^(5*n) / (sqrt(Pi*n) * 3^(3*n)). - Vaclav Kotesovec, Sep 21 2023
From Peter Bala, Sep 24 2023: (Start)
a(n) = A262732(2*n).
a(n) = [x^(2*n)] (1 + 4*x)^((10*n-1)/2) = 16^n * binomial((10*n-1)/2, 2*n).
O.g.f. A(x) = hypergeom([9/10, 7/10, 3/10, 1/10], [5/6, 1/2, 1/6], (12500/27)*x).
(End)
MAPLE
seq( (3*n)!*(10*n)!/((2*n)!*(5*n)!*(6*n)!), n = 0..20); # Peter Bala, Sep 24 2023
PROG
(PARI) a(n) = (3*n)!*(10*n)!/((2*n)!*(5*n)!*(6*n)!); \\ Michel Marcus, Sep 20 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Neven Sajko, Jul 22 2023
STATUS
approved