A216706 a(n) = Product_{k=1..n} (100 - 10/k).

1, 90, 8550, 826500, 80583750, 7897207500, 776558737500, 76546504125000, 7558967282343750, 747497875698437500, 74002289694145312500, 7332954160601671875000, 727184620926332460937500, 72159089307305298046875000, 7164366724082454591796875000

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, A340725.

Programs

Maple

seq(product(100-10/k, k=1.. n), n=0..20);
seq((10^n/n!)*product(10*k+9, k=0.. n-1), n=0..20);

Formula

From Amiram Eldar, Aug 17 2025: (Start)

a(n) = 100^n * Gamma(n+9/10) / (Gamma(9/10) * Gamma(n+1)).

a(n) ~ c * 100^n / n^(1/10), where c = 1/Gamma(9/10) = 1/A340725 = 0.935778... . (End)