A216786 a(n) = Product_{k=1..n} (121 - 11/k).

1, 110, 12705, 1490720, 176277640, 20941783632, 2495562549480, 298041470195040, 35653210872081660, 4270462368900447720, 512028438031163681628, 61443412563739641795360, 7378329792029068652259480, 886534702703800402679177520, 106574136046464005550646840440

Offset: 0

Author

Michel Lagneau, Sep 16 2012

Keywords

• nonn

Comments

This sequence is generalizable: Product_{k=1..n} (q^2 - q/k) = (q^n/n!) * Product_{k=0..n-1} (q*k + q-1) = expansion of (1- x*q^2)^((1-q)/q).

Crossrefs

Cf. A004988, A049382, A004994, A216702, A216703, A216704, A216705, A216706.

Programs

Maple

seq(product(121-11/k, k=1.. n), n=0..20);
seq((11^n/n!)*product(11*k+10, k=0.. n-1), n=0..20);
A216786 := proc(n)
    binomial(-10/11,n)*(-121)^n ;
end proc: # R. J. Mathar, Sep 17 2012

Mathematica

Join[{1},FoldList[Times,121-11/Range[20]]] (* Harvey P. Dale, Mar 15 2016 *)

Formula

From Amiram Eldar, Aug 17 2025: (Start)

a(n) = 121^n * Gamma(n+10/11) / (Gamma(10/11) * Gamma(n+1)).

a(n) ~ c * 121^n / n^(1/11), where c = 1/Gamma(10/11) = 0.942148... . (End)