A147998 [r]*[2r]*[3r]*...[nr], where r=(1+sqrt(5))/2 and []=floor.

1, 3, 12, 72, 576, 5184, 57024, 684288, 9580032, 153280512, 2605768704, 49509605376, 1039701712896, 22873437683712, 548962504409088, 13724062610227200, 370549690476134400, 10745941023807897600, 322378230714236928000, 10316103382855581696000, 340431411634234195968000, 11915099407198196858880000, 440858678066333283778560000, 16752629766520664783585280000, 670105190660826591343411200000

Offset: 1

Author

Clark Kimberling, Jan 22 2011

Keywords

• nonn

Examples

			a(n)=1*3*12*72*...*floor(r*n), where r = golden ratio.
		

Crossrefs

Cf. A000201 (lower Wythoff sequence).

Programs

Mathematica

a[n_]:=Floor[n*(1+5^(1/2))/2];
f[n_]:=Product[a[i],{i,n}];
Table[f[n],{n,1,25}]

Formula

a(n)=[r]*[2r]*[3r]*...[nr], where r=(1+sqrt(5))/2 and []=floor.

a(n) ~ c * r^n * n! / n^(1/(2*r)), where c = 0.7044932... and r = A001622 is the golden ratio. - Vaclav Kotesovec, Aug 19 2024