OFFSET
1,1
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
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..8
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
EXAMPLE
a(2) = a(1)*(a(1)-1)*(a(1)-2)/6 = 5*4*3/6 = 10.
MATHEMATICA
RecurrenceTable[{a[1] == 5, a[n] == a[n - 1](a[n - 1] - 1)(a[n - 1] - 2)/6}, a[n], {n, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Frank M Jackson, Dec 07 2014
STATUS
approved