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