A212307 Numerator of n!/3^n.

1, 1, 2, 2, 8, 40, 80, 560, 4480, 4480, 44800, 492800, 1971200, 25625600, 358758400, 1793792000, 28700672000, 487911424000, 975822848000, 18540634112000, 370812682240000, 2595688775680000, 57105153064960000, 1313418520494080000, 10507348163952640000

Offset: 0

Author

Jean-François Alcover and Paul Curtz, Oct 30 2013

Keywords

• nonn
• frac

Comments

Also the 3rd column of A152656 (or of A216919).

Crossrefs

Cf. A001316, A049606, A125824 (denominators), A152656, A216919.

Cf. A000142, A060828.

Programs

Mathematica

Table[Numerator[n!/3^n], {n, 0, 32}]
(* or *) CoefficientList[Series[Exp[3x], {x, 0, 32}], x] // Denominator

PARI

a(n) = numerator(n!/3^n); \\ Michel Marcus, Oct 30 2013

Formula

a(n) = Product_{i=1..n} A038502(i). - Tom Edgar, Mar 22 2014

a(n) = A000142(n)/A060828(n). - Ridouane Oudra, Sep 23 2024