A364402 a(n) = (3*n)!*(10*n)!/((2*n)!*(5*n)!*(6*n)!).

1, 126, 41990, 15967980, 6421422150, 2663825039876, 1127155102890908, 483537022180231320, 209536624110664757830, 91505601042318156186900, 40205863224219682380130740, 17753412284992688334256754280, 7871411119532225034145860092700, 3502017467737750755575471520717480

Offset: 0

Author

Neven Sajko, Jul 22 2023

Keywords

• nonn

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.

Crossrefs

Bisection of A262732. Cf. A182400, A211419.

Programs

Maple

seq( (3*n)!*(10*n)!/((2*n)!*(5*n)!*(6*n)!), n = 0..20); # Peter Bala, Sep 24 2023

PARI

a(n) = (3*n)!*(10*n)!/((2*n)!*(5*n)!*(6*n)!); \\ Michel Marcus, Sep 20 2023

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)