A216787 a(n) = Product_{k=1..n} (144 - 12/k).

1, 132, 18216, 2550240, 359583840, 50917071744, 7230224187648, 1028757612985344, 146597959850411520, 20914642271992043520, 2986610916440463814656, 426813850967673556058112, 61034380688377318516310016, 8732611390798600956948971520, 1250010944797171165551838494720

Offset

0,2

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).

Links

Table of n, a(n) for n=0..14.

Formula

From Amiram Eldar, Aug 17 2025: (Start)

a(n) = 144^n * Gamma(n+11/12) / (Gamma(11/12) * Gamma(n+1)).

a(n) ~ c * 144^n / n^(1/12), where c = 1/Gamma(11/12) = 0.947376... . (End)

Maple

seq(product(144-12/k, k=1.. n), n=0..20);
seq((12^n/n!)*product(12*k+11, k=0.. n-1), n=0..20);

Mathematica

Join[{1}, FoldList[Times, 144-12/Range[20]]] (* Harvey P. Dale, Dec 22 2015 *)

Crossrefs

Cf. A004988, A049382, A004994, A216702, A216703, A216704, A216705, A216706, A216786.

Sequence in context: A258394 A215546 A269042 * A239817 A175410 A146522

Adjacent sequences: A216784 A216785 A216786 * A216788 A216789 A216790

Keyword

nonn

Author

Michel Lagneau, Sep 16 2012

Status

approved