%I #53 Feb 14 2023 15:03:00

%S 5,10,120,280840,3691654113991480,

%T 8385167839605753859676710992399730619003333960

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

%C 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

%H Vaclav Kotesovec, <a href="/A251702/b251702.txt">Table of n, a(n) for n = 1..8</a>

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

%F a(n) ~ sqrt(6) * A251792^(3^n). - _Vaclav Kotesovec_, Dec 09 2014

%F a(n) = binomial(a(n-1),3) for n >= 1. - _Shel Kaphan_, Feb 06 2023

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

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

%Y Cf. A086714, A251792, A129440, A086714.

%K nonn

%O 1,1

%A _Frank M Jackson_, Dec 07 2014