A251702 a(1)=5, a(n) = a(n-1)*(a(n-1)-1)*(a(n-1)-2)/6.

5, 10, 120, 280840, 3691654113991480, 8385167839605753859676710992399730619003333960

Offset: 1

Author

Frank M Jackson, Dec 07 2014

Keywords

• nonn

Comments

In general, sequence a(n) = binomial(a(n-1),k) is asymptotic to (k!)^(1/(k-1)) * c^(k^n), where the constant c is dependent on k and a(1). For big a(1), c asymptotically approaches (a(1)/(k!)^(1/(k-1)))^(1/k). - Vaclav Kotesovec, Dec 09 2014

Examples

			a(2) = a(1)*(a(1)-1)*(a(1)-2)/6 = 5*4*3/6 = 10.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..8

Crossrefs

Cf. A086714, A251792, A129440, A086714.

Programs

Mathematica

RecurrenceTable[{a[1] == 5, a[n] == a[n - 1](a[n - 1] - 1)(a[n - 1] - 2)/6}, a[n], {n, 10}]

Formula

Limit_{n->oo} a(n)^(1/3^n) = 1.1546796279605837888382808629570944052320556413... (see A251792).

a(n) ~ sqrt(6) * A251792^(3^n). - Vaclav Kotesovec, Dec 09 2014

a(n) = binomial(a(n-1),3) for n >= 1. - Shel Kaphan, Feb 06 2023