A216788 a(n) = Product_{k=1..n} (169 - 13/k).

1, 156, 25350, 4174300, 691890225, 115130533440, 19207610662240, 3210414924974400, 537343198067590200, 90034838076214002400, 15098842345381088202480, 2533860269961226256525280, 425477370330989242241536600, 71480198215606192696578148800

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, A216786, A216787.

Programs

Maple

seq(product(169-13/k, k=1.. n), n=0..20);
seq((13^n/n!)*product(13*k+12, k=0.. n-1), n=0..20);

Mathematica

Table[Product[169-13/k,{k,n}],{n,0,20}] (* Harvey P. Dale, Mar 13 2013 *)

Formula

From Amiram Eldar, Aug 17 2025: (Start)

a(n) = 169^n * Gamma(n+12/13) / (Gamma(12/13) * Gamma(n+1)).

a(n) ~ c * 169^n / n^(1/13), where c = 1/Gamma(12/13) = 0.951742... . (End)